The Fibonacci QuarterlyThe Official Journal of the Fibonacci Association Short Title: Fibonacci Q. Publisher: Taylor & Francis, Abingdon, Oxfordshire; Fibonacci Association, Sun City, AZ ISSN: 0015-0517; 2641-340X/e Online: https://www.tandfonline.com/loi/ufbq20https://www.fq.math.ca/list-of-issues.html Comments: Journal; Indexed cover-to-cover Documents Indexed: 3,067 Publications (since 1963) References Indexed: 95 Publications with 908 References. all top 5 Latest Issues 62, No. 4 (2024) 62, No. 3 (2024) 62, No. 2 (2024) 62, No. 1 (2024) 61, No. 4 (2023) 61, No. 3 (2023) 61, No. 2 (2023) 61, No. 1 (2023) 60, No. 5, Spec. Iss. 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N. S. 13 Đorđević, Gospava B. 13 Komatsu, Takao 13 Křížek, Michal 13 Philippou, Andreas N. 12 Alladi, Krishnaswami 12 Nyblom, Michael A. 12 Zhang, Zhizheng 11 Fielder, Daniel C. 11 Haukkanen, Pentti 11 Shallit, Jeffrey Outlaw 11 Webb, William A. 11 Young, Paul Thomas 10 Ando, Shiro 10 Brown, John L. jun. 10 Chu, Hùng Việt 10 Ewell, John A. 10 Hsu, Leetsch Charles 10 Lengyel, Tamás 10 Wall, Charles R. 9 Anderson, Peter Gordon 9 Cook, Charles K. 9 Greig, W. Elliott 9 Mahon, Brother J. M. 9 Marques, Diego 9 Szalay, László 9 Togbé, Alain 8 Bunder, Martin W. 8 Chuan, Waifong 8 DeLeon, Morris Jack 8 Dilcher, Karl 8 Fennessey, Eric J. 8 Grundman, Helen G. 8 Kennedy, Robert Edward 8 Lind, Douglas A. 8 Pongsriiam, Prapanpong 8 Williams, Hugh Cowie 8 Zhang, Wenpeng 8 Zhao, Fengzhen 7 Atanassov, Krassimir Todorov 7 Gao, Zhenguang 7 Good, Irving John (Jack) 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 Stănică, Pantelimon 7 Wang, Tianming 6 Bacon, Michael R. 6 Church, C. A. jun. 6 Edwards, Kenneth 6 Flórez, Rigoberto 6 Fuller, Leonard E. 6 Hillman, Abraham P. 6 Jacobson, Eliot T. 6 Kilic, Emrah 6 Klaška, Jiří 6 Knopfmacher, Arnold 6 Liptai, Kálmán 6 Liu, Guodong 6 Mizgerd, Clayton M. 6 Monzingo, M. G. 6 Mouline, Mehdi 6 Najar, Rudolph M. ...and 1,852 more Authors all top 5 Fields 2,709 Number theory (11-XX) 697 Combinatorics (05-XX) 92 Special functions (33-XX) 79 Linear and multilinear algebra; matrix theory (15-XX) 60 Sequences, series, summability (40-XX) 55 Probability theory and stochastic processes (60-XX) 43 Computer science (68-XX) 38 Geometry (51-XX) 36 Difference and functional equations (39-XX) 35 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 32 Real functions (26-XX) 31 Information and communication theory, circuits (94-XX) 28 History and biography (01-XX) 27 Numerical analysis (65-XX) 22 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) 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) 7 Operations research, mathematical programming (90-XX) 6 Algebraic geometry (14-XX) 6 Measure and integration (28-XX) 6 Mechanics of particles and systems (70-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 1,562 Publications have been cited 7,353 times in 4,044 Documents Cited by ▼ Year ▼ Some combinatorial identities of Bruckman - a systematic treatment with relation to the older literature. 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Zbl 0467.10009 Gould, H. W. 29 1981 Some identities involving the Fibonacci polynomials. Zbl 1018.11008 Yi, Yuan; Zhang, Wenpeng 28 2002 Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices. Zbl 1079.11012 Lee, Gwang-Yeon; Kim, Jin-Soo; Lee, Sang-Gu 28 2002 Divisibility properties of generalized Fibonacci polynomials. Zbl 0284.10003 Hoggatt, Verner E. jun.; Long, Calvin T. 27 1974 Complex factorizations of the Fibonacci and Lucas numbers. Zbl 1056.11005 Cahill, Nathan D.; D’Errico, John R.; Spence, John P. 27 2003 Some identities involving the Euler and the central factorial numbers. Zbl 0919.11018 Zhang, Wenpeng 27 1998 A second variation on a problem of Diophantus and Davenport. Zbl 0382.10011 Jones, Burton W. 26 1978 Some results on Fibonacci quaternions. Zbl 0186.07801 Iyer, Muthulakshmi R. 25 1969 Some information about the binomial transform. Zbl 0818.05002 Prodinger, Helmut 25 1994 The number of orderings of n candidates when ties are permitted. Zbl 0299.05009 Good, I. J. 24 1975 On weighted \(r\)-generalized Fibonacci sequences. Zbl 0886.11010 Dubeau, François; Motta, Walter; Rachidi, Mustapha; Saeki, Osamu 24 1997 The g.c.d. in Lucas sequences and Lehmer number sequences. Zbl 0732.11008 McDaniel, Wayne L. 24 1991 Fibonacci notes. IV: \(q\)-Fibonacci polynomials. Zbl 0298.10010 Carlitz, Leonard 23 1975 Power digraphs modulo \(n\). Zbl 0936.05049 Wilson, Brad 23 1998 On m-th order linear recurrences. Zbl 0574.10016 Levesque, Claude 23 1985 Fibonacci cubes are the resonance graphs of Fibonaccenes. Zbl 1079.05094 Klavžar, Sandi; Žigert, Petra 23 2005 Sequences, paths, ballot numbers. Zbl 0257.05001 Carlitz, Leonard 22 1972 Derived sequences, the Tribonacci recurrence and cubic forms. Zbl 1001.11008 Elia, Michele 22 2001 The relation of the period modulo to the rank of apparition of m in the Fibonacci sequence. Zbl 0116.03302 Vinson, John 22 1963 On the divisibility properties of Fibonacci numbers. Zbl 0147.02202 Halton, J. H. 21 1966 Fibonacci notes. III: \(q\)-Fibonacci numbers. Zbl 0292.10010 Carlitz, Leonard 21 1974 Generalized quaternions of higher order. Zbl 0407.10014 Iakin, I. L. 21 1977 The bracket function and Fontené-Ward generalized binomial coefficients with application to Fibonomial coefficients. Zbl 0191.32702 Gould, H. W. 21 1969 Divisibility properties of Fibonacci polynomials. Zbl 0211.37303 Webb, W. A.; Parberry, E. A. 21 1969 General Fibonacci sequences in finite groups. Zbl 1006.11500 Aydin, Hüseyin; Dikici, Ramazan 21 1998 Fibonacci and Lucas numbers as tridiagonal matrix determinants. Zbl 1080.11014 Cahill, Nathan D.; Narayan, Darren A. 21 2004 The Fibonacci matrix modulo m. Zbl 0116.03205 Robinson, D. W. 20 1963 On some properties of Humbert’s polynomials. Zbl 0635.33006 Milovanović, G. V.; Djordjević, G. 20 1987 Projective maps of linear recurring sequences with maximal \(p\)-adic periods. Zbl 0761.11007 Huang, Minqiang; Dai, Zongduo 20 1992 Digraphs from powers modulo \(p\). Zbl 0855.05067 Lucheta, Caroline; Miller, Eli; Reiter, Clifford 20 1996 Second derivative sequences of Fibonacci and Lucas polynomials. Zbl 0779.11009 Filipponi, Piero; Horadam, Alwyn F. 20 1993 Some identities involving the Fibonacci numbers and Lucas numbers. Zbl 1052.11012 Zhang, Wenpeng 19 2004 Derivative polynomials for tanh, tan, sech and sec in explicit form. Zbl 1205.11026 Boyadzhiev, Khristo N. 19 2007 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 19 2001 Longest success runs and Fibonacci-type polynomials. Zbl 0575.60022 Philippou, Andreas N.; Makri, Frosso S. 19 1985 Jacobsthal and Pell curves. Zbl 0644.10014 Horadam, Alwyn F. 19 1988 Complex Fibonacci numbers. Zbl 0446.10010 Harman, C. J. 19 1981 Expansion of analytic functions in polynomials associated with Fibonacci numbers. Zbl 0147.06102 Byrd, Paul F. 18 1963 Some results concerning polyominoes. Zbl 0128.24504 Klarner, D. A. 18 1965 Sums of the inverses of binomial coefficients. Zbl 0476.05011 Rockett, Andrew M. 18 1981 Generalized Fibonacci polynomials. Zbl 0274.10022 Hoggatt, V. E. jun.; Bicknell, Marjorie 17 1973 Generalized quaternions with quaternion components. Zbl 0407.10015 Iakin, I. L. 17 1977 Special properties of the sequence \(w_n(a,b; p,q)\). Zbl 0159.05504 Horadam, A. F. 17 1967 On the Fibonacci numbers of trees. Zbl 1133.11011 Zhao, Haixing; Li, Xueliang 17 2006 Analytic continuation of the Fibonacci Dirichlet series. Zbl 1015.11045 Navas, Luis 17 2001 \(q\)-Fibonacci polynomials. Zbl 1027.11011 Cigler, Johann 17 2003 Invariant sequences under binomial transformation. Zbl 0987.05013 Sun, Zhihong 17 2001 Fibonacci balancing numbers. Zbl 1067.11006 Liptai, Kálmán; Kiss, Péter 17 2004 A remark related to the Frobenius problem. Zbl 0766.11014 Brown, Tom C.; Shiue, Peter Jau-Shyong 17 1993 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082 Faye, Bernadette; Luca, Florian 17 2018 The multiparameter noncentral Stirling numbers. Zbl 0802.05003 El-Desouky, B. S. 17 1994 Sequence balancing and cobalancing numbers. Zbl 1214.11027 Panda, G. K. 16 2007 A primer on the Pell sequence and related sequences. Zbl 0319.10013 Bicknell, Marjorie 16 1975 Matrix generators of Pell sequences. Zbl 0399.10011 Ercolano, Joseph 16 1979 Some remarks on the Bell numbers. Zbl 0426.10013 Carlitz, Leonard 16 1980 Gaussian Fibonacci and Lucas numbers. Zbl 0129.02405 Jordan, J. H. 16 1965 Generalized happy numbers. Zbl 1011.11008 Grundman, H. G.; Teeple, E. A. 16 2001 The Filbert matrix. Zbl 0994.11011 Richardson, Thomas M. 16 2001 On the divisibility by 2 of the Stirling numbers of the second kind. Zbl 0808.11017 Lengyel, T. 16 1994 Congruences and recurrences for Bernoulli numbers of higher order. Zbl 0820.11009 Howard, F. T. 16 1994 Associated Stirling numbers. Zbl 0443.10007 Howard, F. T. 16 1980 On the number of summands in Zeckendorf decompositions. Zbl 1225.11021 Koloğlu, Murat; Kopp, Gene S.; Miller, Steven J.; Wang, Yinghui 15 2011 Combinatorial sums and series involving inverses of binomial coefficients. Zbl 0943.11014 Trif, Tiberiu 15 2000 Compositions, partitions, and Fibonacci numbers. Zbl 1259.11028 Sills, Andrew V. 15 2011 A note on generalized Fibonacci numbers. Zbl 0834.11009 Lee, Gwang-Yeon; Lee, Sang-Gu 15 1995 On recurrence formulae for sums involving binomial coefficients. Zbl 1136.40301 Elsner, Carsten 15 2005 The Tetranacci sequence and generalizations. Zbl 0748.11014 Waddill, Marcellus E. 15 1992 Fibonacci words. Zbl 0758.68052 Chuan, Wai-fong 15 1992 Fibonacci numbers and the Rogers-Ramanujan identities. Zbl 1055.11011 Andrews, George E. 15 2004 More sums involving gibonacci polynomial squares revisited. Zbl 1547.11023 Koshy, Thomas 2 2024 Sums involving a class of gibonacci polynomial squares: generalizations. Zbl 1547.11024 Koshy, Thomas 2 2024 Sums involving a class of Jacobsthal polynomial squares. Zbl 1547.11026 Koshy, Thomas; Gao, Zhenguang 1 2024 Sums involving a family of gibonacci polynomial squares: generalizations. Zbl 1547.11025 Koshy, Thomas 1 2024 On certain Fibonacci representations. Zbl 07950825 Liptai, Kálmán; Németh, László; Szakács, Tamás; Szalay, László 1 2024 Additional sums involving gibonacci polynomials. Zbl 1517.11014 Koshy, Thomas 7 2023 Sums involving two classes of Gibonacci polynomials. Zbl 1533.11045 Koshy, Thomas 7 2023 Sums involving gibonacci polynomial squares. Zbl 1520.11024 Koshy, Thomas 7 2023 More sums involving gibonacci polynomial squares. Zbl 1544.11014 Koshy, Thomas 4 2023 Fibonacci or Lucas numbers that are concatenations of two \(g\)-repdigits. Zbl 1518.11016 Adédji, Kouèssi Norbert; Filipin, Alan; Rihane, Salah Eddine; Togbé, Alain 2 2023 Infinite sums involving Gibonacci polynomials revisited: generalizations. Zbl 1533.11043 Koshy, Thomas 2 2023 Infinite sums involving Jacobsthal polynomials: generalizations. Zbl 1533.11044 Koshy, Thomas 2 2023 Sums involving two classes of Gibonacci polynomials revisited. Zbl 1533.11046 Koshy, Thomas 2 2023 Additional sums involving gibonacci polynomial squares. Zbl 1529.11031 Koshy, Thomas 2 2023 Additional sums involving gibonacci polynomials: graph-theoretic confirmations. Zbl 1517.11015 Koshy, Thomas 1 2023 Additional sums involving Gibonacci polynomial squares revisited. Zbl 1533.11047 Koshy, Thomas 1 2023 A note on the Fibonacci sequence and Schreier-type sets. Zbl 1534.11019 Chu, Hùng Việt 1 2023 Sums involving gibonacci polynomial squares: graph-theoretic confirmations. Zbl 1520.11025 Koshy, Thomas 1 2023 Generalized Schreier sets, linear recurrence relation, and Turán graphs. Zbl 1512.11020 Beanland, Kevin; Chu, Hùng Việt; Finch-Smith, Carrie E. 7 2022 Sums involving gibonacci polynomials. Zbl 1508.11025 Koshy, Thomas 6 2022 Infinite sums involving gibonacci polynomials revisited. Zbl 1502.11029 Koshy, Thomas 5 2022 Infinite sums involving gibonacci polynomials. Zbl 1502.11028 Koshy, Thomas 4 2022 Fibonacci along even powers is (almost) realizable. Zbl 1497.11045 Moss, Patrick; Ward, Tom 3 2022 Anti-palindromic compositions. Zbl 1502.05002 Andrews, George E.; Just, Matthew; Simay, Greg 3 2022 \(\mathbb{Q}\)-bonacci words and numbers. Zbl 1517.11012 Kirgizov, Sergey 2 2022 Polyominoes and graphs built from Fibonacci words. Zbl 1514.05033 Kirgizov, Sergey; Ramírez, José L. 2 2022 The Narayana sequence in finite groups. Zbl 1517.11017 Kuloğlu, Bahar; Özkan, Engin; Shannon, Anthony G. 2 2022 The Bergman game. Zbl 1518.91030 Baily, Benjamin; Dell, Justine; Durmić, Irfan; Fleischmann, Henry L.; Jackson, Faye; Mijares, Isaac; Miller, Steven J.; Pesikoff, Ethan; Reifenberg, Luke; Smith Reina, Alicia; Yang, Yingzi 1 2022 An infinite 2-dimensional array associated with electric circuits. Zbl 1520.11021 Evans, Emily; Hendel, Russell Jay 1 2022 Verifying and generalizing Arndt’s compositions. Zbl 1514.05014 Hopkins, Brian; Tangboonduangjit, Aram 1 2022 Generalizing Zeckendorf’s theorem to homogeneous linear recurrences. I. Zbl 1517.11005 Martinez, Thomas C.; Miller, Steven J.; Mizgerd, Clayton; Sun, Chenyang 1 2022 GCD of sums of \(k\) consecutive squares of generalized Fibonacci numbers. Zbl 1520.11028 Mbirika, aBa; Spilker, Jürgen 1 2022 Winning strategies for generalized Zeckendorf games. Zbl 1520.91085 Miller, Steven J.; Sosis, Eliel; Ye, Jingkai 1 2022 On the generalized Tribonacci zeta function. Zbl 1525.11096 Smajlović, Lejla; Šabanac, Zenan; Šćeta, Lamija 1 2022 On the Hurwitz-type zeta function associated to the Lucas sequence. Zbl 1525.11092 Smajlović, Lejla; Šabanac, Zenan; Šćeta, Lamija 1 2022 Infinite sums involving extended gibonacci polynomials. Zbl 1508.11023 Koshy, Thomas 1 2022 Fibonacci summation identities arising from Catalan’s identity. Zbl 1512.11025 Tuenter, Hans J. H. 1 2022 Bounds on Zeckendorf games. Zbl 1497.91062 Cusenza, Anna; Dunkelberg, Aidan; Huffman, Kate; Ke, Dianhui; McClatchey, Micah; Miller, Steven J.; Mizgerd, Clayton; Tiwari, Vashisth; Ye, Jingkai; Zheng, Xiaoyan 1 2022 Generalizing Zeckendorf’s theorem to homogeneous linear recurrences. II. Zbl 1520.11011 Martinez, Thomas C.; Miller, Steven J.; Mizgerd, Clayton; Murphy, Jack; Sun, Chenyang 1 2022 Tetranacci identities via hexagonal tilings. Zbl 1502.11026 Jin, Ziqian (Alexa); Dresden, Greg 1 2022 Weighted sums of Fibonacci and Lucas numbers through colorful tilings. Zbl 1502.11024 Dresden, Greg; Xiao, Yu 1 2022 Sums related to the Fibonacci sequence. Zbl 1502.11027 Kinlaw, Paul; Morris, Michael; Thiagarajan, Samanthak 1 2022 A method for uniformly proving a family of identities. Zbl 1502.11025 Hendel, Russell Jay 1 2022 Infinite sums involving Jacobsthal polynomials. Zbl 1503.11035 Koshy, Thomas 1 2022 Zigzag sequences and representations of integers. Zbl 1503.11014 Campbell, H. E. A.; Wehlau, D. L. 1 2022 Partial sums of the Fibonacci sequence. Zbl 1483.11023 Chu, Hùng Việt 8 2021 How to add two natural numbers in base phi. Zbl 1483.11014 Dekking, F. Michel 4 2021 A simple bijective proof of a familiar derangement recurrence. Zbl 1483.05003 Elizalde, Sergi 3 2021 Exact divisibility by powers of the balancing and Lucas-balancing numbers. Zbl 1484.11053 Patra, Asim; Panda, Gopal Krishna; Khemaratchatakumthorn, Tammatada 3 2021 Infinite sums involving gibonacci polynomial products. Zbl 1503.11031 Koshy, Thomas 2 2021 Graph-theoretic confirmations of four sums of gibonacci polynomial products of order 4. Zbl 1483.11029 Koshy, Thomas 2 2021 In memoriam: Gerald E. Bergum. Zbl 1468.01010 Bicknell-Johnson, Marjorie R. 2 2021 Nondecreasing Deutsch paths. Zbl 1503.05006 Prodinger, Helmut 1 2021 On generalized Zeckendorf decompositions and generalized golden strings. Zbl 1503.11025 Chu, Hùng Việt 1 2021 Winning strategy for multiplayer and multialliance Zeckendorf games. Zbl 1503.91038 Cusenza, Anna; Dunkelberg, Aidan; Huffman, Kate; Ke, Dianhui; Kleber, Daniel; Miller, Steven J.; Mizgerd, Clayton; Tiwari, Vashisth; Ye, Jingkai; Zheng, Xiaoyan 1 2021 Bernoulli and Faulhaber. Zbl 1483.11036 Cereceda, José Luis 1 2021 Various sequences from counting subsets. Zbl 1483.11024 Chu, Hùng Việt 1 2021 A bijection for the Fibonomial coefficients. Zbl 1483.11025 Killpatrick, Kendra; Weaver, Jordan 1 2021 A note on Ledin’s summation problem. Zbl 1486.11026 Shannon, A. G.; Ollerton, R. L. 1 2021 On the \(x\)-coordinates of Pell equations that are products of two Lucas numbers. Zbl 1467.11036 Ddamulira, Mahadi 7 2020 Higher order Fibonacci sequences from generalized Schreier sets. Zbl 1468.11050 Chu, Hùng Việt; Miller, Steven J.; Xiang, Zimu 6 2020 Base phi representations and golden mean beta-expansions. Zbl 1460.11016 Dekking, F. Michel 6 2020 A new combinatorial interpretation of the Fibonacci numbers squared. II. Zbl 1467.05020 Edwards, Kenneth; Allen, Michael A. 6 2020 A new combinatorial interpretation of the Fibonacci numbers cubed. Zbl 1467.05030 Edwards, Kenneth; Allen, Michael A. 5 2020 On the sum of digits of the Zeckendorf representations of two consecutive numbers. Zbl 1468.11025 Shutov, Anton 5 2020 Powers of two in generalized Lucas sequences. Zbl 1468.11060 Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 4 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 4 2020 Counting on Euler and Bernoulli number identities. Zbl 1472.11073 Benjamin, Arthur T.; Lentfer, John; Martinez, Thomas C. 3 2020 On periods of Fibonacci sequences and real quadratic \(p\)-rational fields. Zbl 1470.11021 Bouazzaoui, Zakariae 3 2020 Markoff equation with Pell components. Zbl 1468.11090 Kafle, Bir; Srinivasan, Anitha; Togbé, Alain 3 2020 Matrices in the determinant Hosoya triangle. Zbl 1470.11020 Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara; Ramírez, José L. 2 2020 Linear independence of infinite products generated by the Lucas numbers. Zbl 1471.11218 Duverney, Daniel; Tachiya, Yohei 2 2020 New identities for some symmetric polynomials, and a higher order analogue of the Fibonacci and Lucas numbers. Zbl 1475.11032 Shibukawa, Genki 2 2020 The Markoff-Fibonacci numbers. Zbl 1473.11042 Srinivasan, Anitha 2 2020 Explicit formulas for sums involving the squares of the first \(n\) Tribonacci numbers. Zbl 1468.11061 Schumacher, Raphael 2 2020 Positive integer solutions of some Diophantine equations involving Lucas-balancing numbers. Zbl 1467.11037 Patra, Asim; Panda, G. K. 2 2020 A tiling interpretation of the \(q\)-binomial coefficients. Zbl 1468.05010 Azose, Jonathan J.; Benjamin, Arthur T. 2 2020 Extending Zeckendorf’s theorem to a non-constant recurrence and the Zeckendorf game on this non-constant recurrence relation. Zbl 1465.11053 Bołdyriew, Elżbieta; Cusenza, Anna; Dai, Linglong; Ding, Pei; Dunkelberg, Aidan; Haviland, John; Huffman, Kate; Ke, Dianhui; Kleber, Daniel; Kuretski, Jason; Lentfer, John; Luo, Tianhao; Miller, Steven J.; Mizgerd, Clayton; Tiwari, Vashisth; Ye, Jingkai; Zhang, Yunhao; Zheng, Xiaoyan; Zhu, Weiduo 1 2020 On the relation between Fibonacci and Lucas numbers. Zbl 1470.11024 Dafnis, Spiros D. 1 2020 Recursive triangles appearing embedded in recursive families. Zbl 1470.11041 Hendel, Russell Jay 1 2020 A note on Brousseau’s summation problem. Zbl 1470.11028 Ollerton, R. L.; Shannon, A. G. 1 2020 Girard-Waring type formula for a generalized Fibonacci sequence. Zbl 1467.11024 Wang, Kai 1 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. 1 2020 Congruences involving Euler numbers and power sums. Zbl 1468.11073 McIntosh, Richard J. 1 2020 Generalized Fibonacci sequences in Pythagorean triple preserving matrices. Zbl 1477.11029 Austin, Jathan; Schneider, Lisa 1 2020 A family of lacunary recurrences for Lucas numbers. Zbl 1468.11059 Mahanta, Pankaj Jyoti; Saikia, Manjil P. 1 2020 Independence polynomials of Fibonacci trees are log-concave. Zbl 1475.05092 Bautista-Ramos, César; Guillén-Galvácuten, Carlos; Gómez-Salgado, Paulino 1 2020 Iteration of certain arithmetical functions of particular Lucas sequences. Zbl 1467.11026 Somer, Lawrence; Křížek, Michal 1 2020 Another proof for partial strong divisibility property of Lucas-type polynomials. Zbl 1467.11021 Flórez, Rigoberto; Higuita, Robinson A. 1 2020 On some linear recurrences. Zbl 1467.11014 Lita da Silva, João 1 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 1 2020 The Fibonacci quilt game. Zbl 1469.91018 Miller, Steven J.; Newlon, Alexandra 1 2020 How to sum the squares of the Tetranacci numbers and the Fibonacci \(m\)-step numbers. Zbl 1458.11041 Schumacher, Raphael 8 2019 A new combinatorial interpretation of the Fibonacci numbers squared. Zbl 1437.05043 Edwards, Kenneth; Allen, Michael A. 6 2019 Repdigits as products of balancing and Lucas-balancing numbers with indices in arithmetic progression. Zbl 1457.11016 Rayaguru, Sai Gopal; Panda, Gopal Krishna 6 2019 Combinatorial identities for the Padovan numbers. Zbl 1444.05021 Tedford, Steven J. 6 2019 Sums of squares of Tetranacci numbers: a generating function approach. Zbl 1447.11032 Prodinger, Helmut; Selkirk, Sarah J. 6 2019 Matrices in the Hosoya triangle. Zbl 1447.11021 Blair, Matthew; Flórez, Rigoberto; Mukherjee, Antara 5 2019 Arithmetic functions of Fibonacci and Lucas numbers. Zbl 1475.11031 Jaidee, Montree; Pongsriiam, Prapanpong 5 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 4 2019 ...and 972 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,153 Authors 88 Luca, Florian 47 Kilic, Emrah 45 Kim, Taekyun 42 Chu, Wenchang 40 Kim, Dae San 38 Togbé, Alain 34 Gómez, Carlos Alexis 32 Komatsu, Takao 31 Koshy, Thomas 30 Ramírez, José Luis 29 Soykan, Yüksel 28 Shallit, Jeffrey Outlaw 27 Deveci, Ömür 27 Prodinger, Helmut 26 Belbachir, Hacene 25 Keskin, Refik 24 Włoch, Iwona 23 Bravo, Jhon Jairo 23 Mansour, Toufik 22 He, Tian-Xiao 22 Ray, Prasanta Kumar 22 Sanna, Carlo 22 Szynal-Liana, Anetta 21 Panda, Gopal Krishna 21 Rachidi, Mustapha 21 Simsek, Yilmaz 21 Szalay, László 21 Wagner, Stephan Georg 19 Özkan, Engin 19 Shattuck, Mark A. 18 Miller, Steven J. 18 Rihane, Salah Eddine 18 Trojovský, Pavel 17 Dujella, Andrej 17 Marques, Diego 17 Shiue, Peter Jau-Shyong 16 Qi, Feng 16 Şiar, Zafer 16 Sun, Zhi-Wei 15 Bród, Dorota 15 Dilcher, Karl 15 Fujita, Yasutsugu 15 Klavžar, Sandi 15 Srivastava, Hari Mohan 14 Chuan, Waifong 14 Omur, Nese 14 Qi, Wenfeng 14 Young, Paul Thomas 13 Boussayoud, Ali 13 Egecioglu, Omer 13 Hsu, Leetsch Charles 13 Irmak, Nurettin 13 Jiang, Zhaolin 13 Karaduman, Erdal 13 Pongsriiam, Prapanpong 13 Rout, Sudhansu Sekhar 13 Tan, Elif 13 Tasci, Dursun 12 Catarino, Paula Maria Machado Cruz 12 Cerda-Morales, Gamaliel 12 Dekking, Frederik Michel 12 Goy, Taras P. 12 Ulas, Maciej 11 Bentaher, R. 11 Cheon, Gi-Sang 11 Flórez, Rigoberto 11 Frontczak, Robert 11 Haukkanen, Pentti 11 Kızılateş, Can 11 Koparal, Sibel 11 Rayaguru, Sai Gopal 11 Somer, Lawrence E. 10 Adegoke, Kunle 10 Cipu, Mihai 10 Dolgiĭ, Dmitriĭ Viktorovich 10 Harrington, Joshua 10 Jones, Lenny K. 10 Křížek, Michal 10 Larcombe, Peter J. 10 Mollard, Michel 10 Philippou, Andreas N. 10 Saygı, Elif 10 Sun, Zhihong 10 Yang, Shengliang 9 Akkus, Ilker 9 Andrews, George Eyre 9 Chu, Hùng Việt 9 Fennessey, Eric J. 9 Grundman, Helen G. 9 Herrera, José L. 9 Klaška, Jiří 9 Knopfmacher, Arnold 9 Lengyel, Tamás 9 Liu, Guodong 9 Moll, Victor Hugo 9 Murru, Nadir 9 Sagan, Bruce Eli 9 Saygı, Zülfükar 9 Swamy, Sondekola Rudra 9 Taşkara, Necati ...and 4,053 more Authors all top 5 Cited in 550 Journals 170 Journal of Number Theory 167 Discrete Mathematics 143 Integers 128 Journal of Integer Sequences 95 Discrete Applied Mathematics 87 Linear Algebra and its Applications 79 The Fibonacci Quarterly 75 Applied Mathematics and Computation 66 Rocky Mountain Journal of Mathematics 66 Journal of Combinatorial Theory. 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