# zbMATH — the first resource for mathematics

## The Fibonacci Quarterly

### The Official Journal of the Fibonacci Association

 Short Title: Fibonacci Q. Publisher: Fibonacci Association, Sun City, AZ ISSN: 0015-0517 Online: https://www.fq.math.ca/list-of-issues.html Comments: Indexed cover-to-cover; This journal is available open access.
 Documents Indexed: 2,921 Publications (since 1963)
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#### Latest Issues

 59, No. 2 (2021) 59, No. 1 (2021) 58, No. 5 (2020) 58, No. 4 (2020) 58, No. 3 (2020) 58, No. 2 (2020) 58, No. 1 (2020) 57, No. 5 (2019) 57, No. 4 (2019) 57, No. 3 (2019) 57, No. 2 (2019) 57, No. 1 (2019) 56, No. 4 (2018) 56, No. 3 (2018) 56, No. 2 (2018) 56, No. 1 (2018) 55, No. 5 (2017) 55, No. 4 (2017) 55, No. 3 (2017) 55, No. 2 (2017) 55, No. 1 (2017) 54, No. 4 (2016) 54, No. 3 (2016) 54, No. 2 (2016) 54, No. 1 (2016) 53, No. 4 (2015) 53, No. 3 (2015) 53, No. 2 (2015) 53, No. 1 (2015) 52, No. 5 (2014) 52, No. 4 (2014) 52, No. 3 (2014) 52, No. 2 (2014) 52, No. 1 (2014) 51, No. 4 (2013) 51, No. 3 (2013) 51, No. 2 (2013) 51, No. 1 (2013) 50, No. 4 (2012) 50, No. 3 (2012) 50, No. 2 (2012) 50, No. 1 (2012) 49, No. 4 (2011) 49, No. 3 (2011) 49, No. 2 (2011) 49, No. 1 (2011) 48, No. 4 (2010) 48, No. 3 (2010) 48, No. 2 (2010) 48, No. 1 (2010) 46-47, No. 4 (2009) 46-47, No. 3 (2009) 46-47, No. 2 (2009) 46-47, No. 1 (2009) 45, No. 4 (2007) 45, No. 3 (2007) 45, No. 2 (2007) 45, No. 1 (2007) 44, No. 4 (2006) 44, No. 3 (2006) 44, No. 2 (2006) 44, No. 1 (2006) 43, No. 4 (2005) 43, No. 3 (2005) 43, No. 2 (2005) 43, No. 1 (2005) 42, No. 4 (2004) 42, No. 3 (2004) 42, No. 2 (2004) 42, No. 1 (2004) 41, No. 5 (2003) 41, No. 4 (2003) 41, No. 3 (2003) 41, No. 2 (2003) 41, No. 1 (2003) 40, No. 5 (2002) 40, No. 4 (2002) 40, No. 3 (2002) 40, No. 2 (2002) 40, No. 1 (2002) 39, No. 5 (2001) 39, No. 4 (2001) 39, No. 3 (2001) 39, No. 2 (2001) 39, No. 1 (2001) 38, No. 5 (2000) 38, No. 4 (2000) 38, No. 3 (2000) 38, No. 2 (2000) 38, No. 1 (2000) 37, No. 4 (1999) 37, No. 3 (1999) 37, No. 2 (1999) 37, No. 1 (1999) 36, No. 5 (1998) 36, No. 4 (1998) 36, No. 3 (1998) 36, No. 2 (1998) 36, No. 1 (1998) 35, No. 4 (1997) ...and 70 more Volumes
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#### Authors

 104 Hoggatt, Verner E. jun. 87 Horadam, Alwyn Francis 61 Carlitz, Leonard 52 Shannon, Anthony Greville 42 Bicknell-Johnson, Marjorie R. 41 Kimberling, Clark H. 36 Filipponi, Piero 35 Gould, Henry Wadsworth 34 Somer, Lawrence E. 30 Bicknell, Marjorie 30 Robbins, Neville 27 Luca, Florian 24 Prodinger, Helmut 23 Koshy, Thomas 22 Brousseau, Brother Alfred 21 Arkin, Joseph 21 Miller, Steven J. 20 Bergum, Gerald Edward 19 Bruckman, Paul S. 19 Hirschhorn, Michael D. 17 Howard, Fredric T. 17 Rachidi, Mustapha 16 André-Jeannin, Richard 16 Cooper, Curtis N. 16 Griffiths, Martin 16 Larcombe, Peter J. 16 Long, Calvin T. 15 Panda, Gopal Krishna 14 Benjamin, Arthur T. 14 McDaniel, Wayne L. 14 Swamy, M. N. S. 13 Đorđević, Gospava B. 13 Hendel, Russell Jay 13 Komatsu, Takao 13 Philippou, Andreas N. 12 Alladi, Krishnaswami 12 Zhang, Zhizheng 11 Fielder, Daniel C. 11 Haukkanen, Pentti 11 Křížek, Michal 11 Nyblom, Michael A. 11 Webb, William A. 11 Young, Paul Thomas 10 Ando, Shiro 10 Brown, John L. jun. 10 Ewell, John A. 10 Hsu, Leetsch Charles 10 Shallit, Jeffrey O. 10 Wall, Charles R. 9 Anderson, Peter Gordon 9 Greig, W. Elliott 9 Mahon, Brother J. M. 9 Marques, Diego 8 Ballot, Christian 8 Bunder, Martin W. 8 Chuan, Waifong 8 Cook, Charles K. 8 DeLeon, Morris Jack 8 Dilcher, Karl 8 Fennessey, Eric J. 8 Kennedy, Robert E. 8 Lind, Douglas A. 8 Melham, Ray S. 8 Pongsriiam, Prapanpong 8 Szalay, László 8 Zhang, Wenpeng 8 Zhao, Fengzhen 7 Atanassov, Krassimir Todorov 7 Good, Irving John (Jack) 7 Grundman, Helen G. 7 Hagis, Peter jun. 7 Klarner, David A. 7 Lee, Jack Y. B. 7 Pethe, S. P. 7 Scoville, Richard A. 7 Shiue, Peter Jau-Shyong 7 Spickerman, William R. 7 Wang, Tianming 7 Williams, Hugh Cowie 6 Church, C. A. jun. 6 Fuller, Leonard E. 6 Hillman, Abraham P. 6 Jacobson, Eliot T. 6 Klaška, Jiří 6 Knopfmacher, Arnold 6 Lengyel, Tamás 6 Liu, Guodong 6 Monzingo, M. G. 6 Mouline, Mehdi 6 Najar, Rudolph M. 6 Pla, Juan 6 Reiter, Clifford A. 6 Saeki, Osamu 6 Srinivasa Rao, B. 6 Stănică, Pantelimon 6 Steiner, Ray Phillip 6 Sternheimer, R. M. 6 Tauber, Selmo 6 Taussig Freitag, Herta 6 Togbé, Alain ...and 1,716 more Authors
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#### Fields

 2,537 Number theory (11-XX) 663 Combinatorics (05-XX) 89 Special functions (33-XX) 76 Linear and multilinear algebra; matrix theory (15-XX) 58 Sequences, series, summability (40-XX) 55 Probability theory and stochastic processes (60-XX) 40 Computer science (68-XX) 37 Geometry (51-XX) 34 Difference and functional equations (39-XX) 30 Real functions (26-XX) 28 History and biography (01-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 Information and communication theory, circuits (94-XX) 26 Numerical analysis (65-XX) 19 General and overarching topics; collections (00-XX) 19 Field theory and polynomials (12-XX) 18 Functions of a complex variable (30-XX) 16 Group theory and generalizations (20-XX) 14 Dynamical systems and ergodic theory (37-XX) 13 Statistics (62-XX) 12 Convex and discrete geometry (52-XX) 12 Biology and other natural sciences (92-XX) 9 Approximations and expansions (41-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 6 Algebraic geometry (14-XX) 6 Measure and integration (28-XX) 6 Mechanics of particles and systems (70-XX) 6 Operations research, mathematical programming (90-XX) 5 Mathematical logic and foundations (03-XX) 5 Commutative algebra (13-XX) 5 Integral transforms, operational calculus (44-XX) 4 General topology (54-XX) 4 Manifolds and cell complexes (57-XX) 4 Mathematics education (97-XX) 3 Ordinary differential equations (34-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General algebraic systems (08-XX) 2 Nonassociative rings and algebras (17-XX) 2 Abstract harmonic analysis (43-XX) 2 Astronomy and astrophysics (85-XX) 1 $$K$$-theory (19-XX) 1 Partial differential equations (35-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX)

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1,203 Publications have been cited 4,426 times in 2,571 Documents Cited by Year
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Fibonacci numbers of graphs. Zbl 0475.05046
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1982
Weighted Stirling numbers of the first and second kind. I. Zbl 0428.05003
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1980
Basic properties of a certain generalized sequence of numbers. Zbl 0131.04103
1965
On the square roots of triangular numbers. Zbl 0962.11014
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1999
A note on Fibonacci quaternions. Zbl 0191.32701
Iyer, Mathulakshmi R.
1969
Generalized Fibonacci numbers by matrix methods. Zbl 0472.10016
Kalman, Dan
1982
Solving generalized Fibonacci recurrences. Zbl 0911.11014
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1998
On Euler’s solution of a problem of Diophantus. Zbl 0418.10021
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1979
On generalized Fibonacci quaternions. Zbl 0281.10006
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1973
On the Lucas cubes. Zbl 0987.05048
Munarini, Emanuele; Perelli Cippo, Claudio; Zagaglia Salvi, Norma
2001
The order of the Fibonacci and Lucas numbers. Zbl 0838.11011
Lengyel, T.
1995
The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences. Zbl 0944.05007
Gould, Henry W.
1999
Jacobsthal representation numbers. Zbl 0869.11013
1996
Fibonacci sequences of period $$n$$ in groups. Zbl 0603.10011
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1986
Sums of Fibonacci numbers by matrix methods. Zbl 0539.10013
Er, M. C.
1984
Waiting for the K-th consecutive success and the Fibonacci sequence of order K. Zbl 0476.60008
Philippou, A. N.; Muwafi, A. A.
1982
On the sum of reciprocal Fibonacci numbers. Zbl 1177.11018
Ohtsuka, Hideyuki; Nakamura, Shigeru
2009
The Fibonacci lattice. Zbl 0328.06007
Stanley, Richard P.
1975
Weighted Stirling numbers of the first and second kind. II. Zbl 0441.05003
Carlitz, Leonard
1980
Several identities involving the Fibonacci numbers and Lucas numbers. Zbl 1173.11305
Ma, Rong; Zhang, Wenpeng
2007
Some results on Fibonacci quaternions. Zbl 0186.07801
Iyer, Muthulakshmi R.
1969
Binet’s formula for the Tribonacci sequence. Zbl 0486.10011
Spickerman, W. R.
1982
Some doubly exponential sequences. Zbl 0277.10011
Aho, A. V.; Sloane, N. J. A.
1973
Fibonacci notes. IV: q-Fibonacci polynomials. Zbl 0298.10010
Carlitz, Leonard
1975
A second variation on a problem of Diophantus and Davenport. Zbl 0382.10011
Jones, Burton W.
1978
Fibonacci sequences in finite groups. Zbl 0758.20006
Knox, Steven W.
1992
Some identities involving the Euler and the central factorial numbers. Zbl 0919.11018
Zhang, Wenpeng
1998
Complex factorizations of the Fibonacci and Lucas numbers. Zbl 1056.11005
Cahill, Nathan D.; D’Errico, John R.; Spence, John P.
2003
Divisibility properties of generalized Fibonacci polynomials. Zbl 0284.10003
Hoggatt, Verner E. jun.; Long, Calvin T.
1974
Fibonacci cubes are the resonance graphs of Fibonaccenes. Zbl 1079.05094
Klavžar, Sandi; Žigert, Petra
2005
On the divisibility properties of Fibonacci numbers. Zbl 0147.02202
Halton, J. H.
1966
Roots of Fibonacci polynomials. Zbl 0272.33004
Hoggatt, V. E. jun.; Bicknell, Marjorie
1973
Some identities involving the Fibonacci polynomials. Zbl 1018.11008
Yuan, Yi; Zhang, Wenpeng
2002
On weighted $$r$$-generalized Fibonacci sequences. Zbl 0886.11010
Dubeau, François; Motta, Walter; Rachidi, Mustapha; Saeki, Osamu
1997
Longest success runs and Fibonacci-type polynomials. Zbl 0575.60022
Philippou, Andreas N.; Makri, Frosso S.
1985
Projective maps of linear recurring sequences with maximal $$p$$-adic periods. Zbl 0761.11007
Huang, Minqiang; Dai, Zongduo
1992
The g.c.d. in Lucas sequences and Lehmer number sequences. Zbl 0732.11008
McDaniel, Wayne L.
1991
The relation of the period modulo to the rank of apparition of m in the Fibonacci sequence. Zbl 0116.03302
Vinson, John
1963
Sequences, paths, ballot numbers. Zbl 0257.05001
Carlitz, Leonard
1972
Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices. Zbl 1079.11012
Lee, Gwang-Yeon; Kim, Jin-Soo; Lee, Sang-Gu
2002
Fibonacci and Lucas numbers as tridiagonal matrix determinants. Zbl 1080.11014
Cahill, Nathan D.; Narayan, Darren A.
2004
A history of the Fibonacci Q-matrix and a higher-dimensional problem. Zbl 0467.10009
Gould, H. W.
1981
General Fibonacci sequences in finite groups. Zbl 1006.11500
Aydin, Hüseyin; Dikici, Ramazan
1998
Power digraphs modulo $$n$$. Zbl 0936.05049
1998
Generalized quaternions of higher order. Zbl 0407.10014
Iakin, I. L.
1977
Square Fibonacci numbers, etc. Zbl 0126.07201
Cohn, John H. E.
1964
On the Fibonacci numbers of trees. Zbl 1133.11011
Zhao, Haixing; Li, Xueliang
2006
Fibonacci notes. III: $$q$$-Fibonacci numbers. Zbl 0292.10010
Carlitz, Leonard
1974
Derived sequences, the Tribonacci recurrence and cubic forms. Zbl 1001.11008
Elia, Michele
2001
Some information about the binomial transform. Zbl 0818.05002
Prodinger, Helmut
1994
Invariant sequences under binomial transformation. Zbl 0987.05013
Sun, Zhihong
2001
On m-th order linear recurrences. Zbl 0574.10016
Levesque, Claude
1985
The number of orderings of n candidates when ties are permitted. Zbl 0299.05009
Good, I. J.
1975
Bounds on the Fibonacci number of a maximal outerplanar graph. Zbl 0935.05055
1998
Digraphs from powers modulo $$p$$. Zbl 0855.05067
Lucheta, Caroline; Miller, Eli; Reiter, Clifford
1996
Congruences and recurrences for Bernoulli numbers of higher order. Zbl 0820.11009
Howard, F. T.
1994
Some identities for $$r$$-Fibonacci numbers. Zbl 1264.11008
Howard, F. T.; Cooper, Curtis
2011
The Fibonacci matrix modulo m. Zbl 0116.03205
Robinson, D. W.
1963
Some results concerning polyominoes. Zbl 0128.24504
Klarner, D. A.
1965
The bracket function and Fontené-Ward generalized binomial coefficients with application to Fibonomial coefficients. Zbl 0191.32702
Gould, H. W.
1969
The Filbert matrix. Zbl 0994.11011
Richardson, Thomas M.
2001
Jacobsthal representation polynomials. Zbl 0917.11009
1997
On the divisibility by 2 of the Stirling numbers of the second kind. Zbl 0808.11017
Lengyel, T.
1994
Fibonacci-Lucas quasi-cyclic matrices. Zbl 1081.11011
Lin, Dazheng
2002
Associated Stirling numbers. Zbl 0443.10007
Howard, F. T.
1980
Fibonacci words. Zbl 0758.68052
Chuan, Wai-fong
1992
Some identities involving the Fibonacci numbers and Lucas numbers. Zbl 1052.11012
Zhang, Wenpeng
2004
A primer on the Pell sequence and related sequences. Zbl 0319.10013
Bicknell, Marjorie
1975
Divisibility properties of Fibonacci polynomials. Zbl 0211.37303
Webb, W. A.; Parberry, E. A.
1969
$$q$$-Fibonacci polynomials. Zbl 1027.11011
Cigler, Johann
2003
Generalized quaternions with quaternion components. Zbl 0407.10015
Iakin, I. L.
1977
Fibonacci balancing numbers. Zbl 1067.11006
Liptai, Kálmán; Kiss, Péter
2004
On the Fibonacci number of an M$$\times N$$ lattice. Zbl 0686.05027
1990
Dynamic one-pile Nim. Zbl 1093.91013
Holshouser, Arthur; Reiter, Harold; Rudzinski, James
2003
Optimality proof for the symmetric Fibonacci search technique. Zbl 0144.40705
Avriel, M.; Wilde, D. J.
1966
Derivative polynomials for tanh, tan, sech and sec in explicit form. Zbl 1205.11026
2007
The multiparameter noncentral Stirling numbers. Zbl 0802.05003
El-Desouky, B. S.
1994
Matrix generators of Pell sequences. Zbl 0399.10011
Ercolano, Joseph
1979
Pell and Pell-Lucas polynomials. Zbl 0557.10011
Horadam, Alwyn F.; Mahon, Brother J. M.
1985
On a sum of Melham and its variants. Zbl 1220.11023
Prodinger, Helmut
2009
Divisibility of generalized Fibonacci and Lucas numbers by their subscripts. Zbl 0737.11003
André-Jeannin, Richard
1991
Triple factorization of some Riordan matrices. Zbl 0778.05005
Peart, Paul; Woodson, Leon
1993
Zeckendorf’s theorem and some applications. Zbl 0127.27301
Brown, J. L. jun.
1964
An almost linear recurrence. Zbl 0144.27502
Knuth, Donald E.
1966
The order of appearance of product of consecutive Fibonacci numbers. Zbl 1268.11025
Marques, Diego
2012
Fibonacci representations. Zbl 0167.03901
Carlitz, Leonard
1968
The Binet formula and representations of $$k$$-generalized Fibonacci numbers. Zbl 0989.11008
Lee, Gwang-Yeon; Lee, Sang-Gu; Kim, Jin-Soo; Shin, Hang-Kyun
2001
Analytic continuation of the Fibonacci Dirichlet series. Zbl 1015.11045
Navas, Luis
2001
Chebyshev and Fermat polynomials for diagonal functions. Zbl 0419.10013
1979
The $$p$$-adic valuation of Lucas sequences. Zbl 1400.11053
Sanna, Carlo
2016
A remark related to the Frobenius problem. Zbl 0766.11014
Brown, Tom C.; Shiue, Peter Jau-Shyong
1993
Extended Binet forms for generalized quaternions of higher order. Zbl 0479.10009
Iakin, A. L.
1981
Congruences for Bell and tangent numbers. Zbl 0451.10008
Gessel, Ira
1981
Diophantine representation of Lucas sequences. Zbl 0830.11006
McDaniel, Wayne L.
1995
Fibonacci numbers and the Rogers-Ramanujan identities. Zbl 1055.11011
Andrews, George E.
2004
Another generalized Fibonacci sequence. Zbl 0154.04103
Waddill, Marcellus E.; Sacks, Louis
1967
Fibonacci numbers and generalized binomial coefficients. Zbl 0157.03101
Hoggatt, Verner E. jun.
1967
Special properties of the sequence $$w_ n (a,b; p,q)$$. Zbl 0159.05504
1967
Fibonacci and related sequences in periodic tridiagonal matrices. Zbl 0302.15009
Lehmer, D. H.
1975
On the $$x$$-coordinates of Pell equations that are products of two Lucas numbers. Zbl 1467.11036
2020
Base phi representations and golden mean beta-expansions. Zbl 1460.11016
Dekking, F. Michel
2020
Gaps of summands of the Zeckendorf lattice. Zbl 07240197
Borade, Neelima; Cai, Dexter; Chang, David Z.; Fang, Bruce; Liang, Alex; Miller, Steven J.; Xu, Wanqiao
2020
A new combinatorial interpretation of the Fibonacci numbers squared. II. Zbl 1467.05020
Edwards, Kenneth; Allen, Michael A.
2020
A new combinatorial interpretation of the Fibonacci numbers cubed. Zbl 1467.05030
Edwards, Kenneth; Allen, Michael A.
2020
Explicit formulas for sums involving the squares of the first $$n$$ Tribonacci numbers. Zbl 07315047
Schumacher, Raphael
2020
Central limit theorems for compound paths on the two-dimensional lattice. Zbl 07315049
Fang, Evan; Jenkins, Jonathan; Lee, Zack; Li, Daniel; Lu, Ethan; Miller, Steven J.; Salgado, Dilhan; Siktar, Joshua M.
2020
Markoff equation with Pell components. Zbl 07315050
Kafle, Bir; Srinivasan, Anitha; Togbé, Alain
2020
How to sum the squares of the Tetranacci numbers and the Fibonacci $$m$$-step numbers. Zbl 1458.11041
Schumacher, Raphael
2019
Repdigits as products of balancing and Lucas-balancing numbers with indices in arithmetic progression. Zbl 1457.11016
Rayaguru, Sai Gopal; Panda, Gopal Krishna
2019
The $$p$$-adic valuation of Lucas sequences when $$p$$ is a special prime. Zbl 1447.11019
Ballot, Christian
2019
Sums of squares of Tetranacci numbers: a generating function approach. Zbl 1447.11032
Prodinger, Helmut; Selkirk, Sarah J.
2019
Unified tiling proofs of a family of Fibonacci identities. Zbl 1458.11031
Benjamin, Arthur T.; Crouch, Joshua; Sellers, James A.
2019
Generalized metallic means. Zbl 1458.11033
Gil, Juan B.; Worley, Aaron
2019
Non-classical linear divisibility sequences and cyclotomic polynomials. Zbl 1458.11038
Koshkin, Sergiy
2019
Repdigits in Euler functions of Pell numbers. Zbl 07099281
Sahukar, M. K.; Panda, G. K.
2019
“Choix de Bruxelles”: a new operation on positive integers. Zbl 1457.11014
Angelini, Éric; Blomberg, Lars; Neder, Charlie; Sigrist, Rémy; Sloane, N. J. A.
2019
Gaussian behavior in Zeckendorf decompositions from lattices. Zbl 1456.11019
Chen, Eric; Chen, Robin; Guo, Lucy; Jiang, Cindy; Miller, Steven J.; Siktar, Joshua M.; Yu, Peter
2019
Central limit theorems for gaps of generalized Zeckendorf decompositions. Zbl 1459.60062
Li, Ray; Miller, Steven J.
2019
Arithmetic functions of Fibonacci and Lucas numbers. Zbl 07099364
Jaidee, Montree; Pongsriiam, Prapanpong
2019
Diophantine equations with the Ramanujan $$\tau$$ function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
2019
Alternating offers bargaining and the golden ratio. Zbl 1445.91001
Rachmilevitch, Shiran
2019
The generalized Zeckendorf game. Zbl 1445.91011
Baird-Smith, Paul; Epstein, Alyssa; Flint, Kristen; Miller, Steven J.
2019
Matrices in the Hosoya triangle. Zbl 1447.11021
Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara
2019
A new combinatorial interpretation of the Fibonacci numbers squared. Zbl 1437.05043
Edwards, Kenneth; Allen, Michael A.
2019
Fibonacci and Lucas numbers which have exactly three prime factors and some unique properties of $$F_{18}$$ and $$L_{18}$$. Zbl 1447.11031
Pongsriiam, Prapanpong
2019
Global series for zeta functions. Zbl 1447.11096
Young, Paul Thomas
2019
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
Faye, Bernadette; Luca, Florian
2018
Repdigits as products of consecutive balancing or Lucas-balancing numbers. Zbl 1443.11020
Rayaguru, S. G.; Panda, G. K.
2018
Markov equation with Fibonacci components. Zbl 1458.11056
Luca, Florian; Srinivasan, Anitha
2018
Sequences of consecutive happy numbers in negative bases. Zbl 1448.11016
Grundman, Helen G.; Harris, Pamela E.
2018
The converse of exact divisibility by powers of the Fibonacci and Lucas numbers. Zbl 1443.11017
Onphaeng, Kritkhajohn; Pongsriiam, Prapanpong
2018
Fibonacci-producing rational polynomials. Zbl 1443.11013
Hopkins, Brian; Tangboonduangjit, Aram
2018
The Pascal rhombus and Riordan arrays. Zbl 1443.11023
Yang, Sheng-Liang; Gao, Yuan-Yuan
2018
Circular balancing numbers. Zbl 1401.11046
Panda, A. K.; Panda, G. K.
2017
Fibonacci and Lucas numbers which are one away from their products. Zbl 1401.11048
Pongsriiam, Prapanpong
2017
On generalized multi poly-Euler polynomials. Zbl 1401.11056
Corcino, Roberto B.; Jolany, Hassan; Corcino, Cristina B.; Komatsu, Takao
2017
Polynomial extensions of the Lucas and Ginsburg identities revisited. Zbl 1401.11022
Koshy, Thomas
2017
On moduli for which certain second-order linear recurrences contain a complete system of residues modulo $$m$$. Zbl 1401.11049
Somer, Lawrence; Křížek, Michal
2017
On the masked periodicity of Horadam sequences: a generator-based approach. Zbl 1401.11025
Bagdasar, Ovidiu D.; Larcombe, Peter J.
2017
A bijective proof of a derangement recurrence. Zbl 1400.05030
Benjamin, Arthur T.; Ornstein, Joel
2017
An exploration of sequence A000975. Zbl 1401.11023
Stockmeyer, Paul K.
2017
The Lichtenberg sequence. Zbl 1401.11021
Hinz, Andreas M.
2017
Polynomial extensions of a Diminnie delight. Zbl 1401.11040
Koshy, Thomas; Gao, Zhenguang
2017
Ternary words and Jacobsthal numbers. Zbl 1401.11042
Koshy, Thomas; Grimaldi, Ralph P.
2017
A combinatorial proof for the generating function of powers of the Fibonacci sequence. Zbl 1401.11051
Zhang, Yifan; Grossman, George
2017
Divisibility of the middle Lucasnomial coefficient. Zbl 1401.11052
Ballot, Christian
2017
Some infinite product identities involving Fibonacci and Lucas numbers. Zbl 1401.11024
2017
Generalizations of Delannoy and cross polytope numbers. Zbl 1401.11019
Edwards, Steven; Griffiths, William
2017
On identities of Ruggles, Horadam, Howard, and Young. Zbl 1401.11033
Cooper, Curtis; Miller, Steven; Moses, Peter J. C.; Sahin, Murat; Thanatipanonda, Thotsaporn
2017
Proof and generalization of the Cassini-Catalan-Tagiuri-Gould identities. Zbl 1401.11037
Hendel, Russell Jay
2017
Areas of triangles and other polygons with vertices from various sequences. Zbl 1401.11038
Johnson, Virginia P.; Cook, Charles K.
2017
On the rate of $$p$$-adic convergence of alternating sums of powers of binomial coefficients. Zbl 1401.11054
Lengyel, Tamás
2017
Weighted sums of squares via generalized Eulerian polynomials. Zbl 1401.11057
Pita Ruiz V., Claudio de J.
2017
The $$p$$-adic valuation of Lucas sequences. Zbl 1400.11053
Sanna, Carlo
2016
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2016
Sylvester’s theorem and the non-integrality of a certain binomial sum. Zbl 1400.11061
López-Aguayo, Daniel; Luca, Florian
2016
Some identities involving polynomial coefficients. Zbl 1400.11060
Fahssi, Nour-Eddine
2016
On Franklin and complete magic square matrices. Zbl 1400.05039
Nordgren, Ronald P.
2016
Further physical derivations of Fibonacci summations. Zbl 1400.11057
Treeby, David
2016
Extending some Fibonacci-Lucas relations. Zbl 1400.11041
Edgar, Tom
2016
Hidden formulas in Fibonacci tilings. Zbl 1400.11056
Treeby, David
2016
Some identities for sequences of binomial sums of generalized Fibonacci numbers. Zbl 1400.11038
Cook, Charles K.; Komatsu, Takao
2016
Vieta polynomials and their close relatives. Zbl 1400.11044
Koshy, Thomas
2016
Analogues of a Fibonacci-Lucas identity. Zbl 1400.11035
Bhatnagar, Gaurav
2016
Closed forms for finite sums in which the denominator of the summand is a product of trigonometric functions. Zbl 1400.11077
Melham, R. S.
2016
On a scaled balanced-power product recurrence. Zbl 1400.11045
Larcombe, Peter J.; Fennessey, Eric J.
2016
A combinatorial identity related to cross polytope numbers. Zbl 1400.11059
Edwards, Steven; Griffiths, William
2016
A note on odd perfect numbers. Zbl 1400.11010
Dris, Jose Arnaldo B.; Luca, Florian
2016
Legal decompositions arising from non-positive linear recurrences. Zbl 1400.11037
Catral, Minerva; Ford, Pari L.; Harris, Pamela E.; Miller, Steven J.; Nelson, Dawn
2016
$$p$$-regularity of the $$p$$-adic valuation of the Fibonacci sequence. Zbl 1397.11040
Medina, Luis A.; Rowland, Eric
2015
A note on the invariance of the general $$2\times 2$$ matrix anti-diagonals ratio with increasing matrix power: four proofs. Zbl 1397.11066
Larcombe, Peter J.
2015
The extendibility of $$D(4)$$-pair $$\{F_{2k},5F_{2k}\}$$. Zbl 1397.11070
Filipin, Alan
2015
Divisibility of Fibonomials and Lucasnomials via a general Kummer rule. Zbl 1397.11027
Ballot, Christian
2015
Congruences for partial sums of reciprocals. Zbl 1397.11004
Al-Shaghay, Abdullah; Dilcher, Karl
2015
Graph-theoretic models for the univariate Fibonacci family. Zbl 1397.11035
Koshy, Thomas
2015
The Jacobsthal numbers: two results and two questions. Zbl 1397.11031
Griffiths, Martin; Bramham, Alex
2015
Two remarks on the Collatz cycle conjecture. Zbl 1397.11063
Kaneda, Masayoshi
2015
A condition for anti-diagonals product invariance across powers of $$2\times 2$$ matrix sets characterizing a particular class of polynomial families. Zbl 1397.11067
Larcombe, Peter J.; Fennessey, Eric J.
2015
The Zeckendorf representation of a Beatty-related Fibonacci sum. Zbl 1397.11030
Griffiths, Martin
2015
Perfect balancing numbers. Zbl 1397.11045
Panda, G. K.; Davala, Ravi Kumar
2015
Identically distributed second-order linear recurrences modulo $$p$$. Zbl 1397.11047
Somer, Lawrence; Křížek, Michal
2015
An integral representation for the Fibonacci numbers and their generalization. Zbl 1397.11029
Glasser, M. Lawrence; Zhou, Yajun
2015
Gibonomial coefficients with interesting byproducts. Zbl 1397.11037
Koshy, Thomas
2015
Generalized Bernoulli numbers and a formula of Lucas. Zbl 1397.11054
Moll, Victor H.; Vignat, Christophe
2015
A connection between $$\pi$$ and $$\phi$$. Zbl 1396.11145
Hirschhorn, Michael D.
2015
Members of Lucas sequences whose Euler function is a power of 2. Zbl 1351.11015
Taoufiq Damir, Mohamed; Faye, Bernadette; Luca, Florian; Tall, Amadou
2014
Three series for the generalized golden mean. Zbl 1384.11025
Hare, Kevin; Prodinger, Helmut; Shallit, Jeffrey
2014
Subsequences and divisibility by powers of the Fibonacci numbers. Zbl 1326.11006
Onphaeng, Kritkhajohn; Pongsriiam, Prapanpong
2014
Coincidences in generalized Lucas sequences. Zbl 1375.11014
Bravo, Eric F.; Bravo, Jhon J.; Luca, Florian
2014
The number of differenct parts in the partitions of $$n$$. Zbl 1351.11068
Hirschhorn, Michael D.
2014
New Viète-like infinite products of nested radicals with Fibonacci and Lucas numbers. Zbl 1351.40001
García-Caballero, Esther M.; Moreno, Samuel G.; Prophet, Michael P.
2014
The golden sequence. Zbl 1290.11024
Herrmann, Burghard
2014
A Diophantine equation related to the sum of squares of consecutive $$k$$-generalized Fibonacci numbers. Zbl 1290.11021
Chaves, Ana Paula; Marques, Diego
2014
A generalization of Fibonacci far-difference representations and Gaussian behavior. Zbl 1364.11039
Demontigny, Philippe; Do, Thao; Kulkarni, Archit; Miller, Steven J.; Varma, Umang
2014
Combinatorial proofs of fibonomial identities. Zbl 1396.11029
Benjamin, Arthur T.; Reiland, Elizabeth
2014
Gaussian behavior of the number of summands in Zeckendorf decompositions in small intervals. Zbl 1396.11030
Best, Andrew; Dynes, Patrick; Edelsbrunner, Xixi; McDonald, Brian; Miller, Steven J.; Tor, Kimsy; Turnage-Butterbaugh, Caroline; Weinstein, Madeleine
2014
Fibonacci numbers of the form $$x^{a}\pm x^{b}\pm 1$$. Zbl 1375.11017
Laishram, Shanta; Luca, Florian
2014
Fibonacci numbers close to a power of 2. Zbl 1384.11020
Chern, Shane; Cui, Alvin
2014
Conditions governing cross-family member equality in a particular class of polynomial families. Zbl 1364.11068
Larcombe, Peter J.; Fennessey, Eric J.
2014
...and 752 more Documents
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#### Cited by 2,780 Authors

 56 Luca, Florian 37 Kilic, Emrah 28 Kim, Taekyun 26 Kim, Dae San 25 Chu, Wenchang 23 Togbé, Alain 22 Prodinger, Helmut 21 Ramírez, José Luis 20 Komatsu, Takao 19 Deveci, Ömür 19 Wagner, Stephan G. 17 Shallit, Jeffrey O. 16 Keskin, Refik 16 Panda, Gopal Krishna 15 Shiue, Peter Jau-Shyong 14 Chuan, Waifong 14 Dujella, Andrej 14 Rachidi, Mustapha 14 Sun, Zhi-Wei 13 Gómez, Carlos Alexis 13 Hsu, Leetsch Charles 13 Karaduman, Erdal 13 Klavžar, Sandi 13 Marques, Diego 13 Qi, Wenfeng 13 Srivastava, Hari Mohan 12 Bravo, Jhon Jairo 12 Fujita, Yasutsugu Fujita 12 Ray, Prasanta Kumar 12 Sanna, Carlo 12 Szalay, László 12 Tasci, Dursun 12 Trojovský, Pavel 12 Włoch, Iwona 11 Belbachir, Hacene 11 Jiang, Zhaolin 11 Mansour, Toufik 11 Rout, Sudhansu Sekhar 11 Soykan, Yüksel 11 Young, Paul Thomas 10 Dilcher, Karl 10 He, Tianxiao 10 Shattuck, Mark A. 10 Sun, Zhihong 9 Bentaher, R. 9 Cerda-Morales, Gamaliel Cerda 9 Haukkanen, Pentti 9 Liu, Guodong 9 Miller, Steven J. 9 Özkan, Engin 9 Philippou, Andreas N. 9 Sagan, Bruce Eli 9 Taşkara, Necati 8 Cheon, Gi-Sang 8 Fennessey, Eric J. 8 Larcombe, Peter J. 8 Liu, Wenan 8 Mollard, Michel 8 Omur, Nese 8 Qi, Feng 8 Şiar, Zafer 8 Simsek, Yilmaz 8 Somer, Lawrence E. 7 Akkus, Ilker 7 Arıkan, Talha 7 Bozkurt, Durmuş 7 Catarino, Paula Maria Machado Cruz 7 Cipu, Mihai 7 Dekking, Frederik Michel 7 He, Bo 7 Knopfmacher, Arnold 7 Mező, István 7 Moll, Victor Hugo 7 Plaza, Ángel 7 Wang, Weiping 7 Wituła, Roman 7 Yong, Xuerong 7 Zhang, Wenpeng 7 Zhang, Zhizheng 6 Adelberg, Arnold M. 6 Andrews, George Eyre 6 Brison, Owen J. 6 Egecioglu, Omer 6 El-Desouky, Beih S. 6 Eryılmaz, Serkan N. 6 Falcon, Sergio 6 Flórez, Rigoberto 6 Fraenkel, Aviezri Siegmund 6 Gómez Ruiz, Carlos Alexis 6 Halıcı, Serpil 6 Jang, Gwan-Woo 6 Jones, Lenny K. 6 Koparal, Sibel 6 Křížek, Michal 6 Lengyel, Tamás 6 Li, Shuchao 6 Ma, Shi-Mei 6 Nogueira, Joaquim Eurico 6 Rahmani, Mourad 6 Rayaguru, Sai Gopal ...and 2,680 more Authors
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#### Cited in 407 Journals

 159 Journal of Number Theory 152 Discrete Mathematics 76 Discrete Applied Mathematics 75 Linear Algebra and its Applications 73 Integers 71 Applied Mathematics and Computation 61 Journal of Combinatorial Theory. Series A 58 Journal of Integer Sequences 56 Rocky Mountain Journal of Mathematics 42 The Ramanujan Journal 37 Theoretical Computer Science 36 Journal of Mathematical Analysis and Applications 35 International Journal of Number Theory 34 European Journal of Combinatorics 34 Advances in Difference Equations 32 Mathematics of Computation 31 Advances in Applied Mathematics 28 Advances in Applied Clifford Algebras 25 Chaos, Solitons and Fractals 25 Turkish Journal of Mathematics 23 Finite Fields and their Applications 20 Periodica Mathematica Hungarica 20 Monatshefte für Mathematik 20 Applied Mathematics Letters 18 Journal of Statistical Planning and Inference 18 Indagationes Mathematicae. New Series 17 International Journal of Mathematics and Mathematical Sciences 17 Journal of Computational and Applied Mathematics 17 Transactions of the American Mathematical Society 17 Palestine Journal of Mathematics 16 Czechoslovak Mathematical Journal 16 Abstract and Applied Analysis 15 Proceedings of the American Mathematical Society 15 Annals of Combinatorics 15 Mediterranean Journal of Mathematics 15 Asian-European Journal of Mathematics 14 Computers & Mathematics with Applications 14 Annals of the Institute of Statistical Mathematics 14 Statistics & Probability Letters 14 Graphs and Combinatorics 14 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 14 Journal de Théorie des Nombres de Bordeaux 14 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 13 Proceedings of the Japan Academy. Series A 13 Aequationes Mathematicae 13 Boletín de la Sociedad Matemática Mexicana. Third Series 12 Acta Arithmetica 12 Journal of Mathematical Sciences (New York) 12 Journal of Mathematical Chemistry 12 Special Matrices 11 American Mathematical Monthly 11 Mathematics Magazine 11 Journal of Symbolic Computation 11 Discrete Dynamics in Nature and Society 11 Symmetry 11 International Journal of Advances in Applied Mathematics and Mechanics 10 Indian Journal of Pure & Applied Mathematics 10 The Mathematical Gazette 10 Advances in Mathematics 10 Acta Mathematica Hungarica 10 Mathematical and Computer Modelling 10 Journal of Inequalities and Applications 9 Bulletin of the Australian Mathematical Society 9 Mathematical Notes 9 Mathematica Slovaca 9 Honam Mathematical Journal 9 Journal of Combinatorial Optimization 9 Journal of Applied Mathematics 8 Ukrainian Mathematical Journal 8 Journal of Approximation Theory 8 The Electronic Journal of Combinatorics 8 Mathematical Problems in Engineering 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Communications in Algebra 7 Lithuanian Mathematical Journal 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Results in Mathematics 7 European Journal of Operational Research 7 The Australasian Journal of Combinatorics 7 Acta Mathematica Sinica. English Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Cryptography and Communications 7 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 6 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 6 Archiv der Mathematik 6 Functiones et Approximatio. Commentarii Mathematici 6 Quaestiones Mathematicae 6 Algorithmica 6 Designs, Codes and Cryptography 6 Elemente der Mathematik 6 Experimental Mathematics 6 Statistical Papers 6 Journal of Difference Equations and Applications 6 Acta et Commentationes Universitatis Tartuensis de Mathematica 6 Afrika Matematika 6 Open Mathematics 6 Research in Number Theory 5 Information Processing Letters 5 The Annals of Probability 5 Journal of Algebra ...and 307 more Journals
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#### Cited in 60 Fields

 1,694 Number theory (11-XX) 914 Combinatorics (05-XX) 202 Linear and multilinear algebra; matrix theory (15-XX) 143 Special functions (33-XX) 136 Computer science (68-XX) 109 Probability theory and stochastic processes (60-XX) 74 Group theory and generalizations (20-XX) 73 Numerical analysis (65-XX) 59 Dynamical systems and ergodic theory (37-XX) 58 Information and communication theory, circuits (94-XX) 49 Statistics (62-XX) 48 Functions of a complex variable (30-XX) 48 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 39 Operations research, mathematical programming (90-XX) 36 Biology and other natural sciences (92-XX) 34 Difference and functional equations (39-XX) 29 Real functions (26-XX) 29 Approximations and expansions (41-XX) 27 Sequences, series, summability (40-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 24 Commutative algebra (13-XX) 21 Order, lattices, ordered algebraic structures (06-XX) 20 Field theory and polynomials (12-XX) 18 Algebraic geometry (14-XX) 18 Convex and discrete geometry (52-XX) 16 Geometry (51-XX) 16 Manifolds and cell complexes (57-XX) 15 Statistical mechanics, structure of matter (82-XX) 14 Quantum theory (81-XX) 13 Ordinary differential equations (34-XX) 13 Operator theory (47-XX) 11 Measure and integration (28-XX) 11 Partial differential equations (35-XX) 10 Mathematical logic and foundations (03-XX) 10 Integral transforms, operational calculus (44-XX) 9 Associative rings and algebras (16-XX) 9 Functional analysis (46-XX) 9 Mathematics education (97-XX) 8 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 8 Nonassociative rings and algebras (17-XX) 5 Potential theory (31-XX) 5 Integral equations (45-XX) 4 Category theory; homological algebra (18-XX) 4 Differential geometry (53-XX) 4 Algebraic topology (55-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Abstract harmonic analysis (43-XX) 3 Systems theory; control (93-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 1 General algebraic systems (08-XX) 1 $$K$$-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX)