The Fibonacci QuarterlyThe 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: 2,975 Publications (since 1963) References Indexed: 28 Publications with 285 References. all top 5 Latest Issues 60, No. 4 (2022) 60, No. 3 (2022) 60, No. 2 (2022) 60, No. 1 (2022) 59, No. 4 (2021) 59, No. 3 (2021) 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) ...and 76 more Volumes all top 5 Authors 104 Hoggatt, Verner E. jun. 87 Horadam, Alwyn Francis 61 Carlitz, Leonard 53 Shannon, Anthony Greville 43 Bicknell-Johnson, Marjorie R. 41 Kimberling, Clark H. 38 Koshy, Thomas 36 Filipponi, Piero 36 Somer, Lawrence E. 35 Gould, Henry Wadsworth 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 Křížek, Michal 13 Philippou, Andreas N. 12 Alladi, Krishnaswami 12 Zhang, Zhizheng 11 Fielder, Daniel C. 11 Haukkanen, Pentti 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 Chu, Hùng Việt 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 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 1,759 more Authors all top 5 Fields 2,604 Number theory (11-XX) 679 Combinatorics (05-XX) 90 Special functions (33-XX) 78 Linear and multilinear algebra; matrix theory (15-XX) 59 Sequences, series, summability (40-XX) 55 Probability theory and stochastic processes (60-XX) 40 Computer science (68-XX) 38 Geometry (51-XX) 36 Difference and functional equations (39-XX) 31 Real functions (26-XX) 30 History and biography (01-XX) 30 Game theory, economics, finance, and other social and behavioral sciences (91-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 1,329 Publications have been cited 5,587 times in 3,175 Documents Cited by ▼ Year ▼ Some combinatorial identities of Bruckman - a systematic treatment with relation to the older literature. 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G. 39 1979 The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences. Zbl 0944.05007Gould, Henry W. 37 1999 On the Lucas cubes. Zbl 0987.05048Munarini, Emanuele; Perelli Cippo, Claudio; Zagaglia Salvi, Norma 37 2001 The order of the Fibonacci and Lucas numbers. Zbl 0838.11011Lengyel, T. 33 1995 On the sum of reciprocal Fibonacci numbers. Zbl 1177.11018Ohtsuka, Hideyuki; Nakamura, Shigeru 32 2009 Fibonacci sequences of period \(n\) in groups. Zbl 0603.10011Wilcox, Howard J. 30 1986 Pell and Pell-Lucas polynomials. Zbl 0557.10011Horadam, Alwyn F.; Mahon, Brother J. M. 30 1985 Sums of Fibonacci numbers by matrix methods. Zbl 0539.10013Er, M. C. 29 1984 Weighted Stirling numbers of the first and second kind. II. Zbl 0441.05003Carlitz, Leonard 28 1980 Several identities involving the Fibonacci numbers and Lucas numbers. Zbl 1173.11305Ma, Rong; Zhang, Wenpeng 28 2007 Waiting for the K-th consecutive success and the Fibonacci sequence of order K. Zbl 0476.60008Philippou, A. N.; Muwafi, A. A. 28 1982 The Fibonacci lattice. Zbl 0328.06007Stanley, Richard P. 26 1975 A second variation on a problem of Diophantus and Davenport. Zbl 0382.10011Jones, Burton W. 25 1978 Fibonacci sequences in finite groups. Zbl 0758.20006Knox, Steven W. 25 1992 Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices. Zbl 1079.11012Lee, Gwang-Yeon; Kim, Jin-Soo; Lee, Sang-Gu 25 2002 Binet’s formula for the Tribonacci sequence. Zbl 0486.10011Spickerman, W. R. 25 1982 Some doubly exponential sequences. Zbl 0277.10011Aho, A. V.; Sloane, N. J. A. 24 1973 Some identities involving the Euler and the central factorial numbers. Zbl 0919.11018Zhang, Wenpeng 24 1998 Some identities involving the Fibonacci polynomials. Zbl 1018.11008Yuan, Yi; Zhang, Wenpeng 23 2002 Some results on Fibonacci quaternions. Zbl 0186.07801Iyer, Muthulakshmi R. 23 1969 Complex factorizations of the Fibonacci and Lucas numbers. Zbl 1056.11005Cahill, Nathan D.; D’Errico, John R.; Spence, John P. 22 2003 Fibonacci notes. IV: \(q\)-Fibonacci polynomials. Zbl 0298.10010Carlitz, Leonard 22 1975 Jacobsthal representation polynomials. Zbl 0917.11009Horadam, A. F. 22 1997 A history of the Fibonacci Q-matrix and a higher-dimensional problem. Zbl 0467.10009Gould, H. W. 22 1981 Derived sequences, the Tribonacci recurrence and cubic forms. Zbl 1001.11008Elia, Michele 21 2001 Roots of Fibonacci polynomials. Zbl 0272.33004Hoggatt, V. E. jun.; Bicknell, Marjorie 20 1973 Divisibility properties of generalized Fibonacci polynomials. Zbl 0284.10003Hoggatt, Verner E. jun.; Long, Calvin T. 20 1974 Fibonacci cubes are the resonance graphs of Fibonaccenes. Zbl 1079.05094Klavžar, Sandi; Žigert, Petra 20 2005 On weighted \(r\)-generalized Fibonacci sequences. Zbl 0886.11010Dubeau, François; Motta, Walter; Rachidi, Mustapha; Saeki, Osamu 20 1997 The relation of the period modulo to the rank of apparition of m in the Fibonacci sequence. Zbl 0116.03302Vinson, John 20 1963 On the divisibility properties of Fibonacci numbers. Zbl 0147.02202Halton, J. H. 20 1966 The g.c.d. in Lucas sequences and Lehmer number sequences. Zbl 0732.11008McDaniel, Wayne L. 20 1991 Generalized quaternions of higher order. Zbl 0407.10014Iakin, I. L. 19 1977 Sequences, paths, ballot numbers. Zbl 0257.05001Carlitz, Leonard 19 1972 The number of orderings of n candidates when ties are permitted. Zbl 0299.05009Good, I. J. 19 1975 Power digraphs modulo \(n\). Zbl 0936.05049Wilson, Brad 19 1998 Square Fibonacci numbers, etc. Zbl 0126.07201Cohn, John H. E. 19 1964 Fibonacci notes. III: \(q\)-Fibonacci numbers. Zbl 0292.10010Carlitz, Leonard 18 1974 General Fibonacci sequences in finite groups. Zbl 1006.11500Aydin, Hüseyin; Dikici, Ramazan 18 1998 Invariant sequences under binomial transformation. Zbl 0987.05013Sun, Zhihong 18 2001 Some information about the binomial transform. Zbl 0818.05002Prodinger, Helmut 18 1994 Projective maps of linear recurring sequences with maximal \(p\)-adic periods. Zbl 0761.11007Huang, Minqiang; Dai, Zongduo 18 1992 Fibonacci and Lucas numbers as tridiagonal matrix determinants. Zbl 1080.11014Cahill, Nathan D.; Narayan, Darren A. 18 2004 Longest success runs and Fibonacci-type polynomials. Zbl 0575.60022Philippou, Andreas N.; Makri, Frosso S. 18 1985 Some identities involving the Fibonacci numbers and Lucas numbers. Zbl 1052.11012Zhang, Wenpeng 17 2004 Second derivative sequences of Fibonacci and Lucas polynomials. Zbl 0779.11009Filipponi, Piero; Horadam, Alwyn F. 17 1993 Some results concerning polyominoes. Zbl 0128.24504Klarner, D. A. 17 1965 On m-th order linear recurrences. Zbl 0574.10016Levesque, Claude 17 1985 Complex Fibonacci numbers. Zbl 0446.10010Harman, C. J. 16 1981 On the Fibonacci numbers of trees. Zbl 1133.11011Zhao, Haixing; Li, Xueliang 16 2006 The Fibonacci matrix modulo m. Zbl 0116.03205Robinson, D. W. 16 1963 On the divisibility by 2 of the Stirling numbers of the second kind. Zbl 0808.11017Lengyel, T. 16 1994 The multiparameter noncentral Stirling numbers. Zbl 0802.05003El-Desouky, B. S. 16 1994 Digraphs from powers modulo \(p\). Zbl 0855.05067Lucheta, Caroline; Miller, Eli; Reiter, Clifford 16 1996 Some identities for \(r\)-Fibonacci numbers. Zbl 1264.11008Howard, F. T.; Cooper, Curtis 16 2011 Generalized quaternions with quaternion components. Zbl 0407.10015Iakin, I. L. 15 1977 Associated Stirling numbers. Zbl 0443.10007Howard, F. T. 15 1980 Divisibility properties of Fibonacci polynomials. Zbl 0211.37303Webb, W. A.; Parberry, E. A. 15 1969 The Filbert matrix. Zbl 0994.11011Richardson, Thomas M. 15 2001 Special properties of the sequence \(w_n(a,b; p,q)\). Zbl 0159.05504Horadam, A. F. 15 1967 The \(p\)-adic valuation of Lucas sequences. Zbl 1400.11053Sanna, Carlo 15 2016 Congruences and recurrences for Bernoulli numbers of higher order. Zbl 0820.11009Howard, F. T. 15 1994 The bracket function and Fontené-Ward generalized binomial coefficients with application to Fibonomial coefficients. Zbl 0191.32702Gould, H. W. 14 1969 Bounds on the Fibonacci number of a maximal outerplanar graph. Zbl 0935.05055Alameddine, Ahmad Fawzi 14 1998 Analytic continuation of the Fibonacci Dirichlet series. Zbl 1015.11045Navas, Luis 14 2001 Fibonacci balancing numbers. Zbl 1067.11006Liptai, Kálmán; Kiss, Péter 14 2004 Derivative polynomials for tanh, tan, sech and sec in explicit form. Zbl 1205.11026Boyadzhiev, Khristo N. 14 2007 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 14 2018 Some remarks on the Bell numbers. Zbl 0426.10013Carlitz, Leonard 13 1980 A primer on the Pell sequence and related sequences. Zbl 0319.10013Bicknell, Marjorie 13 1975 Generalized happy numbers. Zbl 1011.11008Grundman, H. G.; Teeple, E. A. 13 2001 Diophantine representation of Lucas sequences. Zbl 0830.11006McDaniel, Wayne L. 13 1995 A note on generalized Fibonacci numbers. Zbl 0834.11009Lee, Gwang-Yeon; Lee, Sang-Gu 13 1995 Sequence balancing and cobalancing numbers. Zbl 1214.11027Panda, G. K. 13 2007 The order of appearance of product of consecutive Fibonacci numbers. Zbl 1268.11025Marques, Diego 13 2012 A remark related to the Frobenius problem. Zbl 0766.11014Brown, Tom C.; Shiue, Peter Jau-Shyong 13 1993 Fibonacci-Lucas quasi-cyclic matrices. Zbl 1081.11011Lin, Dazheng 13 2002 Matrix generators of Pell sequences. Zbl 0399.10011Ercolano, Joseph 12 1979 Chebyshev and Fermat polynomials for diagonal functions. Zbl 0419.10013Horadam, A. F. 12 1979 \(q\)-Fibonacci polynomials. Zbl 1027.11011Cigler, Johann 12 2003 Dynamic one-pile Nim. Zbl 1093.91013Holshouser, Arthur; Reiter, Harold; Rudzinski, James 12 2003 Fibonacci words. Zbl 0758.68052Chuan, Wai-fong 12 1992 Fibonacci numbers and the Rogers-Ramanujan identities. Zbl 1055.11011Andrews, George E. 12 2004 Further properties of Morgan-Voyce polynomials. Zbl 0155.08204Swamy, M. N. S. 12 1968 Vieta polynomials. Zbl 1090.11012Horadam, A. F. 12 2002 Some identities arising from the Fibonacci numbers of certain graphs. Zbl 0548.05035Hopkins, Glenn; Staton, William 12 1984 Gaussian Fibonacci numbers. Zbl 0363.10004Berzsenyi, George 11 1977 A problem of Fermat and the Fibonacci sequence. Zbl 0383.10007Hoggatt, V. E. jun.; Bergum, G. E. 11 1977 Coefficients of the cyclotomic polynomial \(F_{3qr}(x)\). Zbl 0396.10006Beiter, Marion 11 1978 Congruences for Bell and tangent numbers. Zbl 0451.10008Gessel, Ira 11 1981 In memoriam: Gerald E. Bergum. Zbl 1468.01010Bicknell-Johnson, Marjorie R. 2 2021 Exact divisibility by powers of the balancing and Lucas-balancing numbers. Zbl 1484.11053Patra, Asim; Panda, Gopal Krishna; Khemaratchatakumthorn, Tammatada 2 2021 A simple bijective proof of a familiar derangement recurrence. Zbl 1483.05003Elizalde, Sergi 2 2021 A bijection for the Fibonomial coefficients. Zbl 1483.11025Killpatrick, Kendra; Weaver, Jordan 1 2021 Partial sums of the Fibonacci sequence. Zbl 1483.11023Chu, Hùng Việt 1 2021 On generalized Zeckendorf decompositions and generalized golden strings. Zbl 1503.11025Chu, Hùng Việt 1 2021 On the \(x\)-coordinates of Pell equations that are products of two Lucas numbers. Zbl 1467.11036Ddamulira, Mahadi 4 2020 Base phi representations and golden mean beta-expansions. Zbl 1460.11016Dekking, F. Michel 3 2020 An introduction to completeness of positive linear recurrence sequences. Zbl 1465.11054Bołdyriew, Elżbieta; Haviland, John; Lâm, Phúc; Lentfer, John; Miller, Steven J.; Trejos Suárez, Fernando 2 2020 A new combinatorial interpretation of the Fibonacci numbers cubed. Zbl 1467.05030Edwards, Kenneth; Allen, Michael A. 2 2020 Markoff equation with Pell components. Zbl 1468.11090Kafle, Bir; Srinivasan, Anitha; Togbé, Alain 2 2020 Positive integer solutions of some Diophantine equations involving Lucas-balancing numbers. Zbl 1467.11037Patra, Asim; Panda, G. K. 2 2020 A new combinatorial interpretation of the Fibonacci numbers squared. II. Zbl 1467.05020Edwards, Kenneth; Allen, Michael A. 2 2020 Matrices in the determinant Hosoya triangle. Zbl 1470.11020Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara; Ramírez, José L. 1 2020 Linear independence of infinite products generated by the Lucas numbers. Zbl 1471.11218Duverney, Daniel; Tachiya, Yohei 1 2020 Girard-Waring type formula for a generalized Fibonacci sequence. Zbl 1467.11024Wang, Kai 1 2020 Explicit formulas for sums involving the squares of the first \(n\) Tribonacci numbers. Zbl 1468.11061Schumacher, Raphael 1 2020 On the sum of digits of the Zeckendorf representations of two consecutive numbers. Zbl 1468.11025Shutov, Anton 1 2020 Central limit theorems for compound paths on the two-dimensional lattice. Zbl 1468.11052Fang, Evan; Jenkins, Jonathan; Lee, Zack; Li, Daniel; Lu, Ethan; Miller, Steven J.; Salgado, Dilhan; Siktar, Joshua M. 1 2020 Powers of two in generalized Lucas sequences. Zbl 1468.11060Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 1 2020 Congruences involving Euler numbers and power sums. Zbl 1468.11073McIntosh, Richard J. 1 2020 A family of lacunary recurrences for Lucas numbers. Zbl 1468.11059Mahanta, Pankaj Jyoti; Saikia, Manjil P. 1 2020 Independence polynomials of Fibonacci trees are log-concave. Zbl 1475.05092Bautista-Ramos, César; Guillén-Galvácuten, Carlos; Gómez-Salgado, Paulino 1 2020 A tiling interpretation of the \(q\)-binomial coefficients. Zbl 1468.05010Azose, Jonathan J.; Benjamin, Arthur T. 1 2020 Gaps of summands of the Zeckendorf lattice. Zbl 1468.11048Borade, Neelima; Cai, Dexter; Chang, David Z.; Fang, Bruce; Liang, Alex; Miller, Steven J.; Xu, Wanqiao 1 2020 Repdigits as products of balancing and Lucas-balancing numbers with indices in arithmetic progression. Zbl 1457.11016Rayaguru, Sai Gopal; Panda, Gopal Krishna 5 2019 Sums of squares of Tetranacci numbers: a generating function approach. Zbl 1447.11032Prodinger, Helmut; Selkirk, Sarah J. 4 2019 Matrices in the Hosoya triangle. Zbl 1447.11021Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara 4 2019 How to sum the squares of the Tetranacci numbers and the Fibonacci \(m\)-step numbers. Zbl 1458.11041Schumacher, Raphael 4 2019 Unified tiling proofs of a family of Fibonacci identities. Zbl 1458.11031Benjamin, Arthur T.; Crouch, Joshua; Sellers, James A. 3 2019 Arithmetic functions of Fibonacci and Lucas numbers. Zbl 1475.11031Jaidee, Montree; Pongsriiam, Prapanpong 3 2019 The \(p\)-adic valuation of Lucas sequences when \(p\) is a special prime. Zbl 1447.11019Ballot, Christian 3 2019 A new combinatorial interpretation of the Fibonacci numbers squared. Zbl 1437.05043Edwards, Kenneth; Allen, Michael A. 2 2019 Fibonacci and Lucas numbers which have exactly three prime factors and some unique properties of \(F_{18}\) and \(L_{18}\). Zbl 1447.11031Pongsriiam, Prapanpong 2 2019 Generalized metallic means. Zbl 1458.11033Gil, Juan B.; Worley, Aaron 2 2019 Generalizations of Hermite’s identity and applications. Zbl 1458.11005Aursukaree, Saralee; Khemaratchatakumthorn, Tammatada; Pongsriiam, Prapanpong 2 2019 Repdigits in Euler functions of Pell numbers. Zbl 1473.11009Sahukar, M. K.; Panda, G. K. 2 2019 Central limit theorems for gaps of generalized Zeckendorf decompositions. Zbl 1459.60062Li, Ray; Miller, Steven J. 2 2019 Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031Luca, Florian; Mabaso, Sibusiso 2 2019 Combinatorial identities for the Padovan numbers. Zbl 1444.05021Tedford, Steven J. 1 2019 Alternating offers bargaining and the golden ratio. Zbl 1445.91001Rachmilevitch, Shiran 1 2019 The generalized Zeckendorf game. Zbl 1445.91011Baird-Smith, Paul; Epstein, Alyssa; Flint, Kristen; Miller, Steven J. 1 2019 Some high degree generalized Fibonacci identities. Zbl 1447.11024Cooper, Curtis 1 2019 Discovering Fibonacci numbers, Fibonacci words, and a Fibonacci fractal in the tower of Hanoi. Zbl 1447.11029Hinz, Andreas M.; Stockmeyer, Paul K. 1 2019 Global series for zeta functions. Zbl 1447.11096Young, Paul Thomas 1 2019 A non-linear recurrence identity class for terms of a generalized linear recurrence sequence of degree three. Zbl 1458.11027Larcombe, Peter J.; Fennessey, Eric J. 1 2019 Non-classical linear divisibility sequences and cyclotomic polynomials. Zbl 1458.11038Koshkin, Sergiy 1 2019 Linear recurring sequence subgroups in the complex field. II. Zbl 1458.11023Brison, Owen J.; Nogueira, J. Eurico 1 2019 “Choix de Bruxelles”: a new operation on positive integers. Zbl 1457.11014Angelini, Éric; Blomberg, Lars; Neder, Charlie; Sigrist, Rémy; Sloane, N. J. A. 1 2019 Gaussian behavior in Zeckendorf decompositions from lattices. Zbl 1456.11019Chen, Eric; Chen, Robin; Guo, Lucy; Jiang, Cindy; Miller, Steven J.; Siktar, Joshua M.; Yu, Peter 1 2019 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 14 2018 Repdigits as products of consecutive balancing or Lucas-balancing numbers. Zbl 1443.11020Rayaguru, S. G.; Panda, G. K. 9 2018 The converse of exact divisibility by powers of the Fibonacci and Lucas numbers. Zbl 1443.11017Onphaeng, Kritkhajohn; Pongsriiam, Prapanpong 5 2018 Markov equation with Fibonacci components. Zbl 1458.11056Luca, Florian; Srinivasan, Anitha 4 2018 Sequences of consecutive happy numbers in negative bases. Zbl 1448.11016Grundman, Helen G.; Harris, Pamela E. 3 2018 Weighted sums of some second-order sequences. Zbl 1448.11030Adegoke, Kunle 2 2018 Fibonacci-producing rational polynomials. Zbl 1443.11013Hopkins, Brian; Tangboonduangjit, Aram 2 2018 Some new identities for derangement numbers. Zbl 1440.05038Abel, Ulrich 2 2018 \(p\)-adic valuation of Lucas iteration sequences. Zbl 1443.11018Panraksa, Chatchawan; Tangboonduangjit, Aram 2 2018 Conditional (strong) divisibility sequences. Zbl 1444.11033Sahin, Murat; Tan, Elif 1 2018 On the \(D(4)\)-Diophantine triples of Fibonacci numbers. Zbl 1471.11122Rihane, Salah Eddine; Hernane, Mohand Ouamar; Togbé, Alain 1 2018 The sums of the consecutive Fibonacci numbers. Zbl 1448.11044Shtefan, Dmitriy; Dobrovolska, Irina 1 2018 Some Gibonacci convolutions with dividends. Zbl 1448.11041Koshy, Thomas; Griffiths, Martin 1 2018 Arithmetic functions of balancing numbers. Zbl 1448.11009Sahukar, Manasi Kumari; Panda, G. K. 1 2018 The Pascal rhombus and Riordan arrays. Zbl 1443.11023Yang, Sheng-Liang; Gao, Yuan-Yuan 1 2018 Fibonacci and Lucas numbers which are one away from their products. Zbl 1401.11048Pongsriiam, Prapanpong 6 2017 On generalized multi poly-Euler polynomials. Zbl 1401.11056Corcino, Roberto B.; Jolany, Hassan; Corcino, Cristina B.; Komatsu, Takao 4 2017 A bijective proof of a derangement recurrence. Zbl 1400.05030Benjamin, Arthur T.; Ornstein, Joel 4 2017 Circular balancing numbers. Zbl 1401.11046Panda, A. K.; Panda, G. K. 4 2017 The Lichtenberg sequence. Zbl 1401.11021Hinz, Andreas M. 3 2017 An exploration of sequence A000975. Zbl 1401.11023Stockmeyer, Paul K. 3 2017 On moduli for which certain second-order linear recurrences contain a complete system of residues modulo \(m\). Zbl 1401.11049Somer, Lawrence; Křížek, Michal 3 2017 Polynomial extensions of the Lucas and Ginsburg identities revisited. Zbl 1401.11022Koshy, Thomas 2 2017 A combinatorial proof for the generating function of powers of the Fibonacci sequence. Zbl 1401.11051Zhang, Yifan; Grossman, George 2 2017 Divisibility of the middle Lucasnomial coefficient. Zbl 1401.11052Ballot, Christian 2 2017 On the masked periodicity of Horadam sequences: a generator-based approach. Zbl 1401.11025Bagdasar, Ovidiu D.; Larcombe, Peter J. 2 2017 Polynomial extensions of a Diminnie delight. Zbl 1401.11040Koshy, Thomas; Gao, Zhenguang 1 2017 On some arithmetic properties of a sequence related to the quotient of Fibonacci numbers. Zbl 1401.11047Panraksa, Chatchawan; Tangboonduangjit, Aram 1 2017 Integer values of generating functions for the Fibonacci and related sequences. Zbl 1401.11028Bulawa, Andrew; Lee, Whan Ki 1 2017 Ternary words and Jacobsthal numbers. Zbl 1401.11042Koshy, Thomas; Grimaldi, Ralph P. 1 2017 On Candido like identities. Zbl 1401.11031Cerin, Zvonko 1 2017 On identities of Ruggles, Horadam, Howard, and Young. Zbl 1401.11033Cooper, Curtis; Miller, Steven; Moses, Peter J. C.; Sahin, Murat; Thanatipanonda, Thotsaporn 1 2017 Proof and generalization of the Cassini-Catalan-Tagiuri-Gould identities. Zbl 1401.11037Hendel, Russell Jay 1 2017 Areas of triangles and other polygons with vertices from various sequences. Zbl 1401.11038Johnson, Virginia P.; Cook, Charles K. 1 2017 On the rate of \(p\)-adic convergence of alternating sums of powers of binomial coefficients. Zbl 1401.11054Lengyel, Tamás 1 2017 Weighted sums of squares via generalized Eulerian polynomials. Zbl 1401.11057Pita Ruiz V., Claudio de J. 1 2017 Recurrences for entries of powers of matrices. Zbl 1401.11071Stănică, Gabriela N.; Stănică, Pantelimon 1 2017 Congruences for Bernoulli-Lucas sums. Zbl 1401.11058Young, Paul Thomas 1 2017 Closed forms for certain Fibonacci type sums that involve second order products. Zbl 1401.11044Melham, R. S. 1 2017 Some infinite product identities involving Fibonacci and Lucas numbers. Zbl 1401.11024Adegoke, Kunle 1 2017 Generalizations of Delannoy and cross polytope numbers. Zbl 1401.11019Edwards, Steven; Griffiths, William 1 2017 The \(p\)-adic valuation of Lucas sequences. Zbl 1400.11053Sanna, Carlo 15 2016 Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 8 2016 Sylvester’s theorem and the non-integrality of a certain binomial sum. Zbl 1400.11061López-Aguayo, Daniel; Luca, Florian 3 2016 Some identities involving polynomial coefficients. Zbl 1400.11060Fahssi, Nour-Eddine 3 2016 On Franklin and complete magic square matrices. Zbl 1400.05039Nordgren, Ronald P. 2 2016 Further physical derivations of Fibonacci summations. Zbl 1400.11057Treeby, David 2 2016 Extending some Fibonacci-Lucas relations. Zbl 1400.11041Edgar, Tom 1 2016 Hidden formulas in Fibonacci tilings. Zbl 1400.11056Treeby, David 1 2016 Some identities for sequences of binomial sums of generalized Fibonacci numbers. Zbl 1400.11038Cook, Charles K.; Komatsu, Takao 1 2016 ...and 827 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,342 Authors 69 Luca, Florian 41 Kilic, Emrah 40 Kim, Taekyun 37 Kim, Dae San 30 Chu, Wenchang 30 Togbé, Alain 26 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. 19 Mansour, Toufik 19 Panda, Gopal Krishna 19 Ray, Prasanta Kumar 18 Bravo, Jhon Jairo 18 Włoch, Iwona 17 Sanna, Carlo 17 Shiue, Peter Jau-Shyong 17 Trojovský, Pavel 16 Dujella, Andrej 16 Marques, Diego 16 Rachidi, Mustapha 16 Shattuck, Mark A. 15 Belbachir, Hacene 15 Dilcher, Karl 15 Fujita, Yasutsugu Fujita 15 Simsek, Yilmaz 15 Soykan, Yüksel 14 Chuan, Waifong 14 Özkan, Engin 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 Qi, Feng 13 Qi, Wenfeng 13 Szalay, László 13 Tasci, Dursun 13 Young, Paul Thomas 12 Jiang, Zhaolin 12 Miller, Steven J. 12 Rihane, Salah Eddine 12 Rout, Sudhansu Sekhar 12 Szynal-Liana, Anetta 11 Cerda-Morales, Gamaliel Cerda 11 Şiar, Zafer 10 Bród, Dorota 10 Catarino, Paula Maria Machado Cruz 10 Cheon, Gi-Sang 10 Koparal, Sibel 10 Larcombe, Peter J. 10 Mollard, Michel 10 Philippou, Andreas N. 10 Pongsriiam, Prapanpong 10 Sun, Zhihong 9 Bentaher, R. 9 Boussayoud, Ali 9 Cipu, Mihai 9 Fennessey, Eric J. 9 Goy, Taras P. 9 Haukkanen, Pentti 9 Irmak, Nurettin 9 Liu, Guodong 9 Rayaguru, Sai Gopal 9 Sagan, Bruce Eli 9 Taşkara, Necati 8 Akkus, Ilker 8 Andrews, George Eyre 8 Arıkan, Talha 8 Egecioglu, Omer 8 El-Desouky, Beih S. 8 Flórez, Rigoberto 8 Kızılateş, Can 8 Knopfmacher, Arnold 8 Lengyel, Tamás 8 Liu, Wenan 8 Somer, Lawrence E. 8 Tan, Elif 8 Ulas, Maciej 8 Wituła, Roman 8 Włoch, Andrzej 8 Zhang, Zhizheng 7 Adelberg, Arnold M. 7 Bozkurt, Durmuş 7 Dekking, Frederik Michel 7 He, Bo 7 Herrera, José L. 7 Jang, Gwan-Woo 7 Klaška, Jiří 7 Křížek, Michal 7 Mező, István 7 Moll, Victor Hugo 7 Murru, Nadir 7 Plaza, Ángel ...and 3,242 more Authors all top 5 Cited in 464 Journals 163 Journal of Number Theory 160 Discrete Mathematics 98 Integers 82 Discrete Applied Mathematics 79 Linear Algebra and its Applications 78 Journal of Integer Sequences 75 Applied Mathematics and Computation 62 Journal of Combinatorial Theory. Series A 59 Rocky Mountain Journal of Mathematics 49 The Ramanujan Journal 45 Advances in Difference Equations 43 International Journal of Number Theory 39 Journal of Mathematical Analysis and Applications 39 Theoretical Computer Science 36 European Journal of Combinatorics 36 Advances in Applied Mathematics 36 Turkish Journal of Mathematics 34 Periodica Mathematica Hungarica 34 Chaos, Solitons and Fractals 33 Mathematics of Computation 28 Advances in Applied Clifford Algebras 27 Palestine Journal of Mathematics 24 Finite Fields and their Applications 22 The Electronic Journal of Combinatorics 22 Boletín de la Sociedad Matemática Mexicana. Third Series 21 Monatshefte für Mathematik 20 International Journal of Mathematics and Mathematical Sciences 20 Applied Mathematics Letters 20 Journal of Inequalities and Applications 20 Mediterranean Journal of Mathematics 19 Indian Journal of Pure & Applied Mathematics 19 Mathematica Slovaca 19 Indagationes Mathematicae. 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Second Series 11 Symmetry 10 Bulletin of the Australian Mathematical Society 10 Advances in Mathematics 10 Mathematical and Computer Modelling 10 The Australasian Journal of Combinatorics 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 9 Open Mathematics 8 Communications in Algebra 8 Ukrainian Mathematical Journal 8 Journal of Approximation Theory 8 Quaestiones Mathematicae 8 European Journal of Operational Research 8 Journal of Algebraic Combinatorics 8 Mathematical Problems in Engineering 8 Applicable Analysis and Discrete Mathematics 8 Acta Universitatis Sapientiae. Mathematica 8 Cryptography and Communications 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 Experimental Mathematics ...and 364 more Journals all top 5 Cited in 60 Fields 2,148 Number theory (11-XX) 1,110 Combinatorics (05-XX) 260 Linear and multilinear algebra; matrix theory (15-XX) 186 Special functions (33-XX) 155 Computer science (68-XX) 128 Probability theory and stochastic processes (60-XX) 94 Numerical analysis (65-XX) 88 Group theory and generalizations (20-XX) 77 Functions of a complex variable (30-XX) 66 Information and communication theory, circuits (94-XX) 65 Dynamical systems and ergodic theory (37-XX) 59 Statistics (62-XX) 52 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 48 Real functions (26-XX) 44 Operations research, mathematical programming (90-XX) 43 Difference and functional equations (39-XX) 40 Biology and other natural sciences (92-XX) 37 Sequences, series, summability (40-XX) 33 Approximations and expansions (41-XX) 28 Commutative algebra (13-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 24 Field theory and polynomials (12-XX) 23 Order, lattices, ordered algebraic structures (06-XX) 22 Ordinary differential equations (34-XX) 21 Algebraic geometry (14-XX) 21 Convex and discrete geometry (52-XX) 19 Manifolds and cell complexes (57-XX) 18 Geometry (51-XX) 18 Statistical mechanics, structure of matter (82-XX) 17 Partial differential equations (35-XX) 15 Operator theory (47-XX) 15 Quantum theory (81-XX) 13 Associative rings and algebras (16-XX) 13 Nonassociative rings and algebras (17-XX) 12 Integral transforms, operational calculus (44-XX) 12 Integral equations (45-XX) 11 Measure and integration (28-XX) 10 General and overarching topics; collections (00-XX) 10 Mathematical logic and foundations (03-XX) 10 Functional analysis (46-XX) 10 Mathematics education (97-XX) 8 History and biography (01-XX) 6 Systems theory; control (93-XX) 5 Category theory; homological algebra (18-XX) 5 Potential theory (31-XX) 5 Algebraic topology (55-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Mechanics of particles and systems (70-XX) 3 Fluid mechanics (76-XX) 3 Relativity and gravitational theory (83-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Astronomy and astrophysics (85-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) Citations by Year