Results 21 to 30 of about 29,133 (216)
Symmetric and generating functions of generalized (p,q)-numbers
Kuwait Journal of Science, 2021 In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba +2 more
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Notes on generalized and extended Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon +2 more
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On the Inverse of a Fibonacci Number Modulo a Fibonacci Number Being a Fibonacci Number
Mediterranean Journal of Mathematics, 2023 Let $(F_n)_{n \geq 1}$ be the sequence of Fibonacci numbers. For all integers $a$ and $b \geq 1$ with $\gcd(a, b) = 1$, let $[a^{-1} \!\bmod b]$ be the multiplicative inverse of $a$ modulo $b$, which we pick in the usual set of representatives $\{0, 1, \dots, b-1\}$. Put also $[a^{-1} \!\bmod b] := \infty$ when $\gcd(a, b) > 1$.
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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu +3 more
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Periodic words connected with the Fibonacci words
Karpatsʹkì Matematičnì Publìkacìï, 2016 In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and investigated their properties.
G.M. Barabash +2 more
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Curious Generalized Fibonacci Numbers
Mathematics, 2021 A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jose L. Herrera +2 more
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2002 A permutation $ \in S_n$ is said to {\it avoid} a permutation $ \in S_k$ whenever $ $ contains no subsequence with all of the same pairwise comparisons as $ $. For any set $R$ of permutations, we write $S_n(R)$ to denote the set of permutations in $S_n$ which avoid every permutation in $R$. In 1985 Simion and Schmidt showed that $|S_n(132, 213, 123)
Egge, Eric S., Mansour, Toufik
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On Fibonacci functions with Fibonacci numbers [PDF]
Advances in Difference Equations, 2012 Abstract In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R → R such that for all x ∈ R ,
Han, Jeong, Kim, Hee, Neggers, Joseph
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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam +3 more
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Some identities for generalized Fibonacci and Lucas numbers
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana +2 more
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