Results 21 to 30 of about 93 (74)
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
wiley +1 more source
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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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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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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One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
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Copper Lacus Sequence Spaces Associated With Operator Ideals and Their Geometric Properties
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this research, we introduce the regular Copper Lucas matrix operator, which is based on the Copper Lucas sequence. We investigate the sequence spaces c0(Γ) and c(Γ), as well as lpΓ for 1 ≤ p ≤ ∞, all of which are linked to the newly defined regular Copper Lucas matrix Γ.
Shiva Shah +4 more
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Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers
Annales Mathematicae Silesianae, 2023 In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.
Gryszka Karol
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New convolved Fibonacci collocation procedure for the Fitzhugh–Nagumo non-linear equation
Nonlinear EngineeringThis article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo equation. The proposed solution is expressed as a double sum of basis functions that are chosen to be the convolved Fibonacci polynomials that generalize the well-
Abd-Elhameed Waleed Mohamed +2 more
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Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers
Annales Mathematicae SilesianaeA new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
Chimpanzo J. +4 more
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