Results 11 to 20 of about 1,420,930 (275)
Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]
Mathematics, 2018 The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial ...
Ma, Yuankui, Zhang, Wenpeng
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Mathematics, 2021 In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
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On the sum of reciprocal generalized Fibonacci numbers [PDF]
Abstract and Applied Analysis, 2014 In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers.
He, Zilong, Yuan, Pingzhi, Zhuo, Junyi
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On the arrowhead-Fibonacci numbers
Open Mathematics, 2016 AbstractIn this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of thek-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulomand we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers ...
Deveci, Omur, GÜLTEKİN, İnci
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On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
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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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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers [PDF]
, 2005 In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
Egge, Eric C., Mansour, Toufik
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On Bicomplex Fibonacci Numbers and Their Generalization
Models and Theories in Social Systems, 2018 In this chapter, we consider bicomplex numbers with coefficients from Fibonacci sequence and give some identities. Moreover, we demonstrate the accuracy of such identities by taking advantage of idempotent representations of the bicomplex numbers. And then by this representation, we give some identities containing these numbers.
S. Halıcı
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On a problem of Pillai with Fibonacci numbers and powers of 3. [PDF]
Bol Soc Mat Mex, 2020 Consider the sequence $$ \{{F}_{n}\}_{n \ge 0} $$ { F n } n ≥ 0 of Fibonacci numbers defined by $${F}_0=0$$ F 0 = 0 , $${F}_1 =1$$ F 1 = 1 , and $${F}_{{n}+2}= {F}_{{n}+1}+ {F}_{n} $$ F n + 2 = F n + 1 + F n for all $$ n\ge 0 $$ n ≥ 0 . In this paper, we
Ddamulira M.
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The Fibonacci numbers of certain subgraphs of circulant graphs
AKCE International Journal of Graphs and Combinatorics, 2015 The Fibonacci number ℱ(G) of a graph G with vertex set V(G), is the total number of independent vertex sets S⊂V(G); recall that a set S⊂V(G) is said to be independent whenever for every two different vertices u,v∈S there is no edge between them.
Loiret Alejandría Dosal-Trujillo +1 more
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