Results 111 to 120 of about 2,413 (223)
Periodic Coefficients and Random Fibonacci Sequences
, 2012 The random Fibonacci sequence is defined by t_1 = t_2 = 1 and t_n = ± t_{n–1} + t_{n–2} , for n ? 3, where each ± sign is chosen at random with P(+) = P(–) = 1/2. We can think of all possible such sequences as forming a binary tree T.
McLellan, Karyn Anne
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Generalizing Random Fibonacci Sequences
, 2023 We consider generalized Fibonacci sequences with recurrencerelation xn+p+1 = xn+p + xn, which have growth rates of the formlimn→∞ |xn|1/n that behave similarly to the golden ratio, (1 + √5)/2.Following Makover and McGowan’s analysis of the random ...
Sansgiry, Prashant +3 more
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The p-adic valuation of Lucas sequences
, 2016 Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2 − aX − b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms ...
Sanna, Carlo
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Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles
, 2022 In this paper we are going to present three formulas to express Fibonacci-like sequences with the Fibonacci sequence. We constructed Pascal-like triangles using probabilities of a game, and these Pascal-like triangles can be considered generalizations ...
Matsui, Hiroshi, Yamauchi, Toshiyuki
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A Family of Fibonacci-Like Sequences
The Fibonacci Quarterly, 1987 We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_0 = G_1 = 1$, and we express $G_n$ in terms of the Fibonacci numbers $F_n$ and $F_{n-1}$, and in the parameters $\alpha_1,\ldots,\alpha_k$.
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On a generalization of the Hosoya triangle [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Fibonacci polynomial triangle, inspired by the structure of the Hosoya triangle and constructed using Fibonacci polynomials.
Turhan Çifçi +2 more
doaj +1 more source
On the Fibonacci and the Generalized Fibonacci Sequence
Journal of Nepal Mathematical SocietyFibonacci numbers and their sequence are found abundantly in nature. There is a close relation among the Golden, Fibonacci, and Lucas ratios. Such ratios are inherent to design, architecture, construction, and even to the beauty of different natural and manmade solid objects.
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On truncated fibonacci sequences
, 2007 We prove some theorems concerning truncated Fibonacci sequences, which are defined below in Section 2. We also state some conjectures concerning the period (mod m) of truncated Fibonacci sequences, where the integer m is greater than or equal to 2.
Oezkan, Engin
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A class of Fibonacci-type sequences
Discrete Mathematics, 1974 Let \(\{L_n : n\ge 1\}\) be a sequence of the form \[ L_n= \min\left( \sum_{j=1}^p L_{n-a_j}\quad (n>e),\quad \sum_{j=1}^q L_{n-b_j}\quad (n>e)\right), \] where \(\{a_j\}\) and \(\{b_j\}\) are positive integers, and \(e = \max_{i,j} \{a_i ,b_j\}\). A necessary and sufficient condition on the integers \(\{a_j\}\) and \(\{b_j\}\) is given so that, for ...
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Fibonacci Sequences in Finite Groups
, 1990 This paper extend the notion of Fibonacci sequence mod m to Fibonacci sequences in finite ...
Knox, Steven W.
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