Results 101 to 110 of about 879,292 (211)
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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Psychoacoustic Properties of Fibonacci Sequences
Acta Polytechnica, 2008 1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones.
J. Sokoll, S. Fingerhuth
doaj
Generalized Fibonacci Sequences
, 2012 The Fibonacci sequence is famous for possessing wonderful and amazing properties. In this paper, we introduce generalized Fibonacci sequences and related identities consisting even and odd terms.
V K Gupta +2 more
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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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Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles [PDF]
, 2017 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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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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Binomial Sums Involving Second-Order Linearly Recurrent Sequences
Consider the sequences ( U-n : n is an element of N-0 ) and ( V-n : n is an element of N) satisfying the second order linear recurrences U-n = pU(n-1) + Un-2 and V-n = pV (n-1) + Vn-2 with the initial conditions U-0 = 0, U-1 = 1, V-0 = 2, and V-1 = p. We
Kılıç, Emrah, Campbell, John m.
core
, 1981 The matrices of Fibonacci numbers (called windows) possess some unusual properties which are not shared by normal matrices, such as commutativity under multiplication and +1 for all determinants.
M.C. Er
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Closed forms for finite sums of weighted products of generalized Fibonacci numbers [PDF]
, 2017 In this paper, we present closed forms for certain finite sums of weighted products of generalized Fibonacci numbers. Indeed, we present seven multi-parameter families of such finite sums, all of which we believe to be new. In each of these families, the
Melham, RS
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Unique Properties of the Fibonacci and Lucas Sequences [PDF]
, 2017 The algebraic structure of the set of all Fibonacci-like sequences, which includes the Fibonacci and Lucas sequences, is developed, utilizing an isomorphism between this set and a subset of the 2 by 2 integer matrices.
Parry, Stephen
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