Results 1 to 10 of about 48,003 (223)
Curious Generalized Fibonacci Numbers [PDF]
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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On the Sum of Reciprocal Generalized Fibonacci Numbers [PDF]
Abstract and Applied Analysis, 2014 We consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
Pingzhi Yuan, Zilong He, Junyi Zhou
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]
Mathematica Bohemica, 2022 We consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis +3 more
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Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices [PDF]
Linear and multilinear algebra, 2021 By considering the tiling of an N-board (a linear array of N square cells of unit width) with new types of tile that we refer to as combs, we give a combinatorial interpretation of the product of two consecutive generalized Fibonacci numbers $ s_n $ sn (
Michael Allen, Kenneth Edwards
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers [PDF]
, 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)
Eric S. Egge, Toufik Mansour
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Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant [PDF]
Symmetry, 2021 Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity.
V. Faraoni, Farah Atieh
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“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials
Journal of Physics: Conference Series, 2022 Many researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields.
Mannu Arya, V. Verma
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Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and\n Generalized Fibonacci Polynomial Sequences [PDF]
Kyungpook mathematical journal, 2012 In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, $m$ and derive certain interesting properties related to them.
Alexandre Laugier, Manjil P. Saikia
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On Generalized Fibonacci Numbers
Communications in Advanced Mathematical Sciences, 2020 Fibonacci numbers and their polynomials have been generalized mainly by two ways: by maintaining the recurrence relation and varying the initial conditions, and by varying the recurrence relation and maintaining the initial conditions. In this paper, we
Isaac Owino Okoth, Fidel Oduol
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