## 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: 2,965 Publications (since 1963) References Indexed: 19 Publications with 186 References.
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### Latest Issues

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### Authors

 104 Hoggatt, Verner E. jun. 87 Horadam, Alwyn Francis 61 Carlitz, Leonard 53 Shannon, Anthony Greville 42 Bicknell-Johnson, Marjorie R. 41 Kimberling, Clark H. 36 Filipponi, Piero 35 Gould, Henry Wadsworth 35 Koshy, Thomas 34 Somer, Lawrence E. 30 Bicknell, Marjorie 30 Robbins, Neville 28 Luca, Florian 26 Prodinger, Helmut 25 Miller, Steven J. 22 Brousseau, Brother Alfred 21 Arkin, Joseph 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 Hendel, Russell Jay 14 McDaniel, Wayne L. 14 Swamy, M. N. S. 13 Đorđević, Gospava B. 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 Lengyel, Tamás 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 Edward 8 Lind, Douglas A. 8 Melham, Ray S. 8 Pongsriiam, Prapanpong 8 Szalay, László 8 Williams, Hugh Cowie 8 Zhang, Wenpeng 8 Zhao, Fengzhen 7 Atanassov, Krassimir Todorov 7 Chu, Hùng Việt 7 Good, Irving John (Jack) 7 Grundman, Helen G. 7 Hagis, Peter jun. 7 Klarner, David Anthony 7 Lee, Jack Y. B. 7 Ollerton, Richard L. 7 Pethe, S. P. 7 Scoville, Richard A. 7 Shiue, Peter Jau-Shyong 7 Spickerman, William R. 7 Togbé, Alain 7 Wang, Tianming 6 Church, C. A. jun. 6 Fuller, Leonard E. 6 Hillman, Abraham P. 6 Jacobson, Eliot T. 6 Klaška, Jiří 6 Knopfmacher, Arnold 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. ...and 1,750 more Authors
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### Fields

 2,587 Number theory (11-XX) 669 Combinatorics (05-XX) 90 Special functions (33-XX) 77 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) 31 Real functions (26-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 History and biography (01-XX) 28 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) 17 Functions of a complex variable (30-XX) 16 Group theory and generalizations (20-XX) 15 Dynamical systems and ergodic theory (37-XX) 13 Statistics (62-XX) 13 Biology and other natural sciences (92-XX) 12 Convex and discrete geometry (52-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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Fibonacci numbers of graphs. Zbl 0475.05046
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Weighted Stirling numbers of the first and second kind. I. Zbl 0428.05003
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A note on Fibonacci quaternions. Zbl 0191.32701
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Solving generalized Fibonacci recurrences. Zbl 0911.11014
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Generalized Fibonacci numbers by matrix methods. Zbl 0472.10016
Kalman, Dan
1982
Jacobsthal representation numbers. Zbl 0869.11013
1996
The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences. Zbl 0944.05007
Gould, Henry W.
1999
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
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2001
The order of the Fibonacci and Lucas numbers. Zbl 0838.11011
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On the sum of reciprocal Fibonacci numbers. Zbl 1177.11018
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2009
Fibonacci sequences of period $$n$$ in groups. Zbl 0603.10011
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Sums of Fibonacci numbers by matrix methods. Zbl 0539.10013
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1984
Several identities involving the Fibonacci numbers and Lucas numbers. Zbl 1173.11305
Ma, Rong; Zhang, Wenpeng
2007
Weighted Stirling numbers of the first and second kind. II. Zbl 0441.05003
Carlitz, Leonard
1980
Waiting for the K-th consecutive success and the Fibonacci sequence of order K. Zbl 0476.60008
Philippou, A. N.; Muwafi, A. A.
1982
Pell and Pell-Lucas polynomials. Zbl 0557.10011
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1985
A second variation on a problem of Diophantus and Davenport. Zbl 0382.10011
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1978
Binet’s formula for the Tribonacci sequence. Zbl 0486.10011
Spickerman, W. R.
1982
Some doubly exponential sequences. Zbl 0277.10011
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1973
Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices. Zbl 1079.11012
Lee, Gwang-Yeon; Kim, Jin-Soo; Lee, Sang-Gu
2002
Some results on Fibonacci quaternions. Zbl 0186.07801
Iyer, Muthulakshmi R.
1969
Some identities involving the Fibonacci polynomials. Zbl 1018.11008
Yuan, Yi; Zhang, Wenpeng
2002
Fibonacci sequences in finite groups. Zbl 0758.20006
Knox, Steven W.
1992
The Fibonacci lattice. Zbl 0328.06007
Stanley, Richard P.
1975
Jacobsthal representation polynomials. Zbl 0917.11009
1997
Fibonacci notes. IV: $$q$$-Fibonacci polynomials. Zbl 0298.10010
Carlitz, Leonard
1975
Complex factorizations of the Fibonacci and Lucas numbers. Zbl 1056.11005
Cahill, Nathan D.; D’Errico, John R.; Spence, John P.
2003
Some identities involving the Euler and the central factorial numbers. Zbl 0919.11018
Zhang, Wenpeng
1998
On weighted $$r$$-generalized Fibonacci sequences. Zbl 0886.11010
Dubeau, François; Motta, Walter; Rachidi, Mustapha; Saeki, Osamu
1997
A history of the Fibonacci Q-matrix and a higher-dimensional problem. Zbl 0467.10009
Gould, H. W.
1981
Roots of Fibonacci polynomials. Zbl 0272.33004
Hoggatt, V. E. jun.; Bicknell, Marjorie
1973
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
The relation of the period modulo to the rank of apparition of m in the Fibonacci sequence. Zbl 0116.03302
Vinson, John
1963
On the divisibility properties of Fibonacci numbers. Zbl 0147.02202
Halton, J. H.
1966
The g.c.d. in Lucas sequences and Lehmer number sequences. Zbl 0732.11008
McDaniel, Wayne L.
1991
Derived sequences, the Tribonacci recurrence and cubic forms. Zbl 1001.11008
Elia, Michele
2001
Generalized quaternions of higher order. Zbl 0407.10014
Iakin, I. L.
1977
General Fibonacci sequences in finite groups. Zbl 1006.11500
Aydin, Hüseyin; Dikici, Ramazan
1998
Fibonacci notes. III: $$q$$-Fibonacci numbers. Zbl 0292.10010
Carlitz, Leonard
1974
Fibonacci and Lucas numbers as tridiagonal matrix determinants. Zbl 1080.11014
Cahill, Nathan D.; Narayan, Darren A.
2004
Square Fibonacci numbers, etc. Zbl 0126.07201
Cohn, John H. E.
1964
Longest success runs and Fibonacci-type polynomials. Zbl 0575.60022
Philippou, Andreas N.; Makri, Frosso S.
1985
Some information about the binomial transform. Zbl 0818.05002
Prodinger, Helmut
1994
Power digraphs modulo $$n$$. Zbl 0936.05049
1998
Invariant sequences under binomial transformation. Zbl 0987.05013
Sun, Zhihong
2001
Sequences, paths, ballot numbers. Zbl 0257.05001
Carlitz, Leonard
1972
Some identities involving the Fibonacci numbers and Lucas numbers. Zbl 1052.11012
Zhang, Wenpeng
2004
Some results concerning polyominoes. Zbl 0128.24504
Klarner, D. A.
1965
Projective maps of linear recurring sequences with maximal $$p$$-adic periods. Zbl 0761.11007
Huang, Minqiang; Dai, Zongduo
1992
Second derivative sequences of Fibonacci and Lucas polynomials. Zbl 0779.11009
Filipponi, Piero; Horadam, Alwyn F.
1993
The number of orderings of n candidates when ties are permitted. Zbl 0299.05009
Good, I. J.
1975
The Fibonacci matrix modulo m. Zbl 0116.03205
Robinson, D. W.
1963
On m-th order linear recurrences. Zbl 0574.10016
Levesque, Claude
1985
Some identities for $$r$$-Fibonacci numbers. Zbl 1264.11008
Howard, F. T.; Cooper, Curtis
2011
On the divisibility by 2 of the Stirling numbers of the second kind. Zbl 0808.11017
Lengyel, T.
1994
The multiparameter noncentral Stirling numbers. Zbl 0802.05003
El-Desouky, B. S.
1994
Congruences and recurrences for Bernoulli numbers of higher order. Zbl 0820.11009
Howard, F. T.
1994
Digraphs from powers modulo $$p$$. Zbl 0855.05067
Lucheta, Caroline; Miller, Eli; Reiter, Clifford
1996
Associated Stirling numbers. Zbl 0443.10007
Howard, F. T.
1980
Divisibility properties of Fibonacci polynomials. Zbl 0211.37303
Webb, W. A.; Parberry, E. A.
1969
On the Fibonacci numbers of trees. Zbl 1133.11011
Zhao, Haixing; Li, Xueliang
2006
The $$p$$-adic valuation of Lucas sequences. Zbl 1400.11053
Sanna, Carlo
2016
Bounds on the Fibonacci number of a maximal outerplanar graph. Zbl 0935.05055
1998
The Filbert matrix. Zbl 0994.11011
Richardson, Thomas M.
2001
Analytic continuation of the Fibonacci Dirichlet series. Zbl 1015.11045
Navas, Luis
2001
Generalized quaternions with quaternion components. Zbl 0407.10015
Iakin, I. L.
1977
Complex Fibonacci numbers. Zbl 0446.10010
Harman, C. J.
1981
The bracket function and Fontené-Ward generalized binomial coefficients with application to Fibonomial coefficients. Zbl 0191.32702
Gould, H. W.
1969
Generalized happy numbers. Zbl 1011.11008
Grundman, H. G.; Teeple, E. A.
2001
A note on generalized Fibonacci numbers. Zbl 0834.11009
Lee, Gwang-Yeon; Lee, Sang-Gu
1995
Some remarks on the Bell numbers. Zbl 0426.10013
Carlitz, Leonard
1980
Fibonacci balancing numbers. Zbl 1067.11006
Liptai, Kálmán; Kiss, Péter
2004
Fibonacci-Lucas quasi-cyclic matrices. Zbl 1081.11011
Lin, Dazheng
2002
Sequence balancing and cobalancing numbers. Zbl 1214.11027
Panda, G. K.
2007
A remark related to the Frobenius problem. Zbl 0766.11014
Brown, Tom C.; Shiue, Peter Jau-Shyong
1993
A primer on the Pell sequence and related sequences. Zbl 0319.10013
Bicknell, Marjorie
1975
Derivative polynomials for tanh, tan, sech and sec in explicit form. Zbl 1205.11026
2007
The order of appearance of product of consecutive Fibonacci numbers. Zbl 1268.11025
Marques, Diego
2012
Diophantine representation of Lucas sequences. Zbl 0830.11006
McDaniel, Wayne L.
1995
Matrix generators of Pell sequences. Zbl 0399.10011
Ercolano, Joseph
1979
Dynamic one-pile Nim. Zbl 1093.91013
Holshouser, Arthur; Reiter, Harold; Rudzinski, James
2003
Fibonacci numbers and the Rogers-Ramanujan identities. Zbl 1055.11011
Andrews, George E.
2004
Special properties of the sequence $$w_n(a,b; p,q)$$. Zbl 0159.05504
1967
$$q$$-Fibonacci polynomials. Zbl 1027.11011
Cigler, Johann
2003
Fibonacci words. Zbl 0758.68052
Chuan, Wai-fong
1992
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
Faye, Bernadette; Luca, Florian
2018
Application of Markov chains properties to $$r$$-generalized Fibonacci sequences. Zbl 0937.11004
Mouline, Mehdi; Rachidi, Mustapha
1999
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
A problem of Fermat and the Fibonacci sequence. Zbl 0383.10007
Hoggatt, V. E. jun.; Bergum, G. E.
1977
Coefficients of the cyclotomic polynomial $$F_{3qr}(x)$$. Zbl 0396.10006
Beiter, Marion
1978
Chebyshev and Fermat polynomials for diagonal functions. Zbl 0419.10013
1979
Zeckendorf’s theorem and some applications. Zbl 0127.27301
Brown, J. L. jun.
1964
Optimality proof for the symmetric Fibonacci search technique. Zbl 0144.40705
Avriel, M.; Wilde, D. J.
1966
Divisibility of generalized Fibonacci and Lucas numbers by their subscripts. Zbl 0737.11003
André-Jeannin, Richard
1991
Exact divisibility by powers of the balancing and Lucas-balancing numbers. Zbl 1484.11053
Patra, Asim; Panda, Gopal Krishna; Khemaratchatakumthorn, Tammatada
2021
A simple bijective proof of a familiar derangement recurrence. Zbl 1483.05003
Elizalde, Sergi
2021
On generalized Zeckendorf decompositions and generalized golden strings. Zbl 07528780
Chu, Hùng Việt
2021
A bijection for the Fibonomial coefficients. Zbl 1483.11025
Killpatrick, Kendra; Weaver, Jordan
2021
Partial sums of the Fibonacci sequence. Zbl 1483.11023
Chu, Hùng Việt
2021
On the $$x$$-coordinates of Pell equations that are products of two Lucas numbers. Zbl 1467.11036
2020
Positive integer solutions of some Diophantine equations involving Lucas-balancing numbers. Zbl 1467.11037
Patra, Asim; Panda, G. K.
2020
Base phi representations and golden mean beta-expansions. Zbl 1460.11016
Dekking, F. Michel
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
Markoff equation with Pell components. Zbl 1468.11090
Kafle, Bir; Srinivasan, Anitha; Togbé, Alain
2020
A tiling interpretation of the $$q$$-binomial coefficients. Zbl 1468.05010
Azose, Jonathan J.; Benjamin, Arthur T.
2020
Gaps of summands of the Zeckendorf lattice. Zbl 1468.11048
Borade, Neelima; Cai, Dexter; Chang, David Z.; Fang, Bruce; Liang, Alex; Miller, Steven J.; Xu, Wanqiao
2020
Matrices in the determinant Hosoya triangle. Zbl 1470.11020
Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara; Ramírez, José L.
2020
An introduction to completeness of positive linear recurrence sequences. Zbl 1465.11054
Bołdyriew, Elżbieta; Haviland, John; Lâm, Phúc; Lentfer, John; Miller, Steven J.; Trejos Suárez, Fernando
2020
Linear independence of infinite products generated by the Lucas numbers. Zbl 1471.11218
Duverney, Daniel; Tachiya, Yohei
2020
Girard-Waring type formula for a generalized Fibonacci sequence. Zbl 1467.11024
Wang, Kai
2020
Explicit formulas for sums involving the squares of the first $$n$$ Tribonacci numbers. Zbl 1468.11061
Schumacher, Raphael
2020
On the sum of digits of the Zeckendorf representations of two consecutive numbers. Zbl 1468.11025
Shutov, Anton
2020
Central limit theorems for compound paths on the two-dimensional lattice. Zbl 1468.11052
Fang, Evan; Jenkins, Jonathan; Lee, Zack; Li, Daniel; Lu, Ethan; Miller, Steven J.; Salgado, Dilhan; Siktar, Joshua M.
2020
Powers of two in generalized Lucas sequences. Zbl 1468.11060
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
2020
Congruences involving Euler numbers and power sums. Zbl 1468.11073
McIntosh, Richard J.
2020
A family of lacunary recurrences for Lucas numbers. Zbl 1468.11059
Mahanta, Pankaj Jyoti; Saikia, Manjil P.
2020
Repdigits as products of balancing and Lucas-balancing numbers with indices in arithmetic progression. Zbl 1457.11016
Rayaguru, Sai Gopal; Panda, Gopal Krishna
2019
Unified tiling proofs of a family of Fibonacci identities. Zbl 1458.11031
Benjamin, Arthur T.; Crouch, Joshua; Sellers, James A.
2019
How to sum the squares of the Tetranacci numbers and the Fibonacci $$m$$-step numbers. Zbl 1458.11041
Schumacher, Raphael
2019
Arithmetic functions of Fibonacci and Lucas numbers. Zbl 1475.11031
Jaidee, Montree; Pongsriiam, Prapanpong
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
Generalized metallic means. Zbl 1458.11033
Gil, Juan B.; Worley, Aaron
2019
Repdigits in Euler functions of Pell numbers. Zbl 1473.11009
Sahukar, M. K.; Panda, G. K.
2019
Central limit theorems for gaps of generalized Zeckendorf decompositions. Zbl 1459.60062
Li, Ray; Miller, Steven J.
2019
Diophantine equations with the Ramanujan $$\tau$$ function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
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
A non-linear recurrence identity class for terms of a generalized linear recurrence sequence of degree three. Zbl 1458.11027
Larcombe, Peter J.; Fennessey, Eric J.
2019
Non-classical linear divisibility sequences and cyclotomic polynomials. Zbl 1458.11038
Koshkin, Sergiy
2019
Generalizations of Hermite’s identity and applications. Zbl 1458.11005
Aursukaree, Saralee; Khemaratchatakumthorn, Tammatada; Pongsriiam, Prapanpong
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
Combinatorial identities for the Padovan numbers. Zbl 1444.05021
Tedford, Steven J.
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
Some high degree generalized Fibonacci identities. Zbl 1447.11024
Cooper, Curtis
2019
Discovering Fibonacci numbers, Fibonacci words, and a Fibonacci fractal in the tower of Hanoi. Zbl 1447.11029
Hinz, Andreas M.; Stockmeyer, Paul K.
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
The converse of exact divisibility by powers of the Fibonacci and Lucas numbers. Zbl 1443.11017
Onphaeng, Kritkhajohn; Pongsriiam, Prapanpong
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
Fibonacci-producing rational polynomials. Zbl 1443.11013
Hopkins, Brian; Tangboonduangjit, Aram
2018
Some new identities for derangement numbers. Zbl 1440.05038
Abel, Ulrich
2018
$$p$$-adic valuation of Lucas iteration sequences. Zbl 1443.11018
Panraksa, Chatchawan; Tangboonduangjit, Aram
2018
Conditional (strong) divisibility sequences. Zbl 1444.11033
Sahin, Murat; Tan, Elif
2018
On the $$D(4)$$-Diophantine triples of Fibonacci numbers. Zbl 1471.11122
Rihane, Salah Eddine; Hernane, Mohand Ouamar; Togbé, Alain
2018
The sums of the consecutive Fibonacci numbers. Zbl 1448.11044
Shtefan, Dmitriy; Dobrovolska, Irina
2018
Some Gibonacci convolutions with dividends. Zbl 1448.11041
Koshy, Thomas; Griffiths, Martin
2018
Arithmetic functions of balancing numbers. Zbl 1448.11009
Sahukar, Manasi Kumari; Panda, G. K.
2018
Weighted sums of some second-order sequences. Zbl 1448.11030
2018
The Pascal rhombus and Riordan arrays. Zbl 1443.11023
Yang, Sheng-Liang; Gao, Yuan-Yuan
2018
Fibonacci and Lucas numbers which are one away from their products. Zbl 1401.11048
Pongsriiam, Prapanpong
2017
A bijective proof of a derangement recurrence. Zbl 1400.05030
Benjamin, Arthur T.; Ornstein, Joel
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
Circular balancing numbers. Zbl 1401.11046
Panda, A. K.; Panda, G. K.
2017
The Lichtenberg sequence. Zbl 1401.11021
Hinz, Andreas M.
2017
On generalized multi poly-Euler polynomials. Zbl 1401.11056
Corcino, Roberto B.; Jolany, Hassan; Corcino, Cristina B.; Komatsu, Takao
2017
An exploration of sequence A000975. Zbl 1401.11023
Stockmeyer, Paul K.
2017
Polynomial extensions of the Lucas and Ginsburg identities revisited. Zbl 1401.11022
Koshy, Thomas
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
On the masked periodicity of Horadam sequences: a generator-based approach. Zbl 1401.11025
Bagdasar, Ovidiu D.; Larcombe, Peter J.
2017
Ternary words and Jacobsthal numbers. Zbl 1401.11042
Koshy, Thomas; Grimaldi, Ralph P.
2017
Closed forms for certain Fibonacci type sums that involve second order products. Zbl 1401.11044
Melham, R. S.
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
Polynomial extensions of a Diminnie delight. Zbl 1401.11040
Koshy, Thomas; Gao, Zhenguang
2017
On some arithmetic properties of a sequence related to the quotient of Fibonacci numbers. Zbl 1401.11047
Panraksa, Chatchawan; Tangboonduangjit, Aram
2017
Integer values of generating functions for the Fibonacci and related sequences. Zbl 1401.11028
Bulawa, Andrew; Lee, Whan Ki
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
Recurrences for entries of powers of matrices. Zbl 1401.11071
Stănică, Gabriela N.; Stănică, Pantelimon
2017
Congruences for Bernoulli-Lucas sums. Zbl 1401.11058
Young, Paul Thomas
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
...and 824 more Documents
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### Cited by 3,241 Authors

 67 Luca, Florian 41 Kilic, Emrah 39 Kim, Taekyun 36 Kim, Dae San 30 Togbé, Alain 28 Chu, Wenchang 25 Gómez, Carlos Alexis 25 Prodinger, Helmut 25 Ramírez, José Luis 22 Deveci, Ömür 22 Komatsu, Takao 20 Keskin, Refik 20 Shallit, Jeffrey O. 20 Wagner, Stephan G. 18 Bravo, Jhon Jairo 18 Panda, Gopal Krishna 18 Ray, Prasanta Kumar 17 Mansour, Toufik 17 Sanna, Carlo 17 Shiue, Peter Jau-Shyong 17 Trojovský, Pavel 17 Włoch, Iwona 16 Dujella, Andrej 16 Marques, Diego 16 Rachidi, Mustapha 15 Dilcher, Karl 14 Belbachir, Hacene 14 Chuan, Waifong 14 Fujita, Yasutsugu Fujita 14 Srivastava, Hari Mohan 14 Sun, Zhi-Wei 13 He, Tianxiao 13 Hsu, Leetsch Charles 13 Karaduman, Erdal 13 Klavžar, Sandi 13 Omur, Nese 13 Özkan, Engin 13 Qi, Wenfeng 13 Shattuck, Mark A. 13 Szalay, László 13 Tasci, Dursun 13 Young, Paul Thomas 12 Jiang, Zhaolin 12 Qi, Feng 12 Rihane, Salah Eddine 12 Rout, Sudhansu Sekhar 12 Simsek, Yilmaz 12 Soykan, Yüksel 11 Cerda-Morales, Gamaliel Cerda 11 Miller, Steven J. 11 Szynal-Liana, Anetta 10 Cheon, Gi-Sang 10 Koparal, Sibel 10 Larcombe, Peter J. 10 Mollard, Michel 10 Philippou, Andreas N. 10 Şiar, Zafer 10 Sun, Zhihong 9 Bentaher, R. 9 Cipu, Mihai 9 Fennessey, Eric J. 9 Haukkanen, Pentti 9 Irmak, Nurettin 9 Liu, Guodong 9 Pongsriiam, Prapanpong 9 Sagan, Bruce Eli 9 Taşkara, Necati 8 Akkus, Ilker 8 Andrews, George Eyre 8 Arıkan, Talha 8 Catarino, Paula Maria Machado Cruz 8 Egecioglu, Omer 8 El-Desouky, Beih S. 8 Goy, Taras P. 8 Kızılateş, Can 8 Knopfmacher, Arnold 8 Liu, Wenan 8 Rayaguru, Sai Gopal 8 Somer, Lawrence E. 8 Tan, Elif 8 Ulas, Maciej 8 Wituła, Roman 8 Włoch, Andrzej 8 Zhang, Zhizheng 7 Bozkurt, Durmuş 7 Bród, Dorota 7 Dekking, Frederik Michel 7 Flórez, Rigoberto 7 He, Bo 7 Herrera, José L. 7 Jang, Gwan-Woo 7 Klaška, Jiří 7 Křížek, Michal 7 Lengyel, Tamás 7 Mező, István 7 Moll, Victor Hugo 7 Murru, Nadir 7 Plaza, Ángel 7 Rahmani, Mourad 7 Sezer, Mehmet ...and 3,141 more Authors
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### Cited in 453 Journals

 161 Journal of Number Theory 159 Discrete Mathematics 95 Integers 79 Discrete Applied Mathematics 79 Linear Algebra and its Applications 77 Journal of Integer Sequences 74 Applied Mathematics and Computation 62 Journal of Combinatorial Theory. Series A 59 Rocky Mountain Journal of Mathematics 47 The Ramanujan Journal 45 Advances in Difference Equations 41 International Journal of Number Theory 39 Journal of Mathematical Analysis and Applications 39 Theoretical Computer Science 36 European Journal of Combinatorics 36 Turkish Journal of Mathematics 35 Advances in Applied Mathematics 34 Periodica Mathematica Hungarica 34 Chaos, Solitons and Fractals 32 Mathematics of Computation 28 Advances in Applied Clifford Algebras 27 Palestine Journal of Mathematics 23 Finite Fields and their Applications 22 Boletín de la Sociedad Matemática Mexicana. Third Series 21 Monatshefte für Mathematik 21 The Electronic Journal of Combinatorics 20 International Journal of Mathematics and Mathematical Sciences 20 Applied Mathematics Letters 20 Journal of Inequalities and Applications 19 Indagationes Mathematicae. New Series 19 Mediterranean Journal of Mathematics 18 Journal of Statistical Planning and Inference 18 Mathematica Slovaca 18 Asian-European Journal of Mathematics 17 Czechoslovak Mathematical Journal 17 Journal of Computational and Applied Mathematics 17 Proceedings of the American Mathematical Society 17 Transactions of the American Mathematical Society 17 Filomat 17 Annals of Combinatorics 17 Hacettepe Journal of Mathematics and Statistics 16 Indian Journal of Pure & Applied Mathematics 16 Statistics & Probability Letters 16 Abstract and Applied Analysis 16 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 15 American Mathematical Monthly 15 Acta Mathematica Hungarica 15 Journal de Théorie des Nombres de Bordeaux 15 Special Matrices 15 AIMS Mathematics 14 Computers & Mathematics with Applications 14 Annals of the Institute of Statistical Mathematics 14 Graphs and Combinatorics 14 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 13 The Mathematical Gazette 13 Proceedings of the Japan Academy. Series A 13 Aequationes Mathematicae 13 JP Journal of Algebra, Number Theory and Applications 12 Acta Arithmetica 12 The Fibonacci Quarterly 12 Journal of Mathematical Sciences (New York) 12 Journal of Difference Equations and Applications 12 Journal of Mathematical Chemistry 12 Discrete Dynamics in Nature and Society 12 Afrika Matematika 11 Mathematical Notes 11 Mathematics Magazine 11 Journal of Symbolic Computation 11 Symmetry 11 International Journal of Advances in Applied Mathematics and Mechanics 10 Bulletin of the Australian Mathematical Society 10 Advances in Mathematics 10 Results in Mathematics 10 Mathematical and Computer Modelling 10 The Australasian Journal of Combinatorics 10 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 10 Research in Number Theory 9 Honam Mathematical Journal 9 Journal of Combinatorial Optimization 9 Acta et Commentationes Universitatis Tartuensis de Mathematica 9 Journal of Applied Mathematics 9 Journal of Applied Mathematics & Informatics 8 Ukrainian Mathematical Journal 8 Journal of Approximation Theory 8 Quaestiones Mathematicae 8 Mathematical Problems in Engineering 8 Journal of Discrete Mathematical Sciences & Cryptography 8 Cryptography and Communications 8 Open Mathematics 7 Communications in Algebra 7 Lithuanian Mathematical Journal 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Algorithmica 7 European Journal of Operational Research 7 Experimental Mathematics 7 Statistical Papers 7 Acta Mathematica Sinica. English Series 7 Annales Mathematicae Silesianae 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris ...and 353 more Journals
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### Cited in 60 Fields

 2,074 Number theory (11-XX) 1,073 Combinatorics (05-XX) 255 Linear and multilinear algebra; matrix theory (15-XX) 180 Special functions (33-XX) 152 Computer science (68-XX) 125 Probability theory and stochastic processes (60-XX) 87 Numerical analysis (65-XX) 84 Group theory and generalizations (20-XX) 75 Functions of a complex variable (30-XX) 63 Dynamical systems and ergodic theory (37-XX) 62 Information and communication theory, circuits (94-XX) 57 Statistics (62-XX) 52 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 46 Real functions (26-XX) 42 Difference and functional equations (39-XX) 42 Operations research, mathematical programming (90-XX) 38 Biology and other natural sciences (92-XX) 36 Sequences, series, summability (40-XX) 33 Approximations and expansions (41-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 27 Commutative algebra (13-XX) 23 Order, lattices, ordered algebraic structures (06-XX) 22 Field theory and polynomials (12-XX) 22 Algebraic geometry (14-XX) 21 Convex and discrete geometry (52-XX) 20 Ordinary differential equations (34-XX) 18 Geometry (51-XX) 18 Manifolds and cell complexes (57-XX) 18 Statistical mechanics, structure of matter (82-XX) 16 Operator theory (47-XX) 15 Partial differential equations (35-XX) 14 Quantum theory (81-XX) 13 Integral transforms, operational calculus (44-XX) 11 Associative rings and algebras (16-XX) 11 Nonassociative rings and algebras (17-XX) 11 Measure and integration (28-XX) 10 General and overarching topics; collections (00-XX) 10 Functional analysis (46-XX) 9 Mathematics education (97-XX) 8 History and biography (01-XX) 8 Mathematical logic and foundations (03-XX) 8 Integral equations (45-XX) 5 Potential theory (31-XX) 5 Algebraic topology (55-XX) 5 Systems theory; control (93-XX) 4 Category theory; homological algebra (18-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Fluid mechanics (76-XX) 3 Relativity and gravitational theory (83-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-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)