Results 31 to 40 of about 1,099 (82)
The Generalization of Gaussians and Leonardo’s Octonions
Annales Mathematicae Silesianae, 2023 In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented.
Vieira Renata Passos Machado +3 more
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A curious property of series involving terms of generalized sequences
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 1, Page 55-63, 2000., 2000 Here we are concerned with series involving generalized Fibonacci numbers Un (p, q) and generalized Lucas numbers Vn (p, q). The aim of this paper is to find triples (p, q, r) for which the series Un (p, q)/rn and Vn (p, q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n.
Odoardo Brugia, Piero Filipponi
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On the power sum problem of Lucas polynomials and its divisible property
Open Mathematics, 2018 The main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.
Xiao Wang
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On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
Open Mathematics, 2021 In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata +3 more
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Stability of second‐order recurrences modulo pr
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 4, Page 225-241, 2000., 2000 The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p‐stable if the set of residue frequencies of the sequence reduced modulo pr is eventually constant as a function of r. The authors identify and characterize the stability of second‐order recurrences modulo odd primes.
Lawrence Somer, Walter Carlip
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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Invariance of recurrence sequences under a galois group
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 327-334, 1996., 1995 Let F be a Galois field of order q, k a fixed positive integer and R = Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F‐vector space Γk(F)( = Γ(L)) of all sequences over Fk×1 is a left R‐module. For any regular f(D) ∈ R, Ωk(f(D)) = {S ∈ Γk(F) : f(D)S
Hassan Al-Zaid, Surjeet Singh
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A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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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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Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
, 2010 We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers.
Asmussen +9 more
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