Results 81 to 90 of about 320 (182)
A Note on Incomplete Fibonacci–Lucas Relations
, 2023 We define the incomplete generalized bivariate Fibonacci p-polynomials and the incomplete generalized bivariate Lucas p-polynomials. We study their recursive relations and derive an interesting relationship through their generating functions ...
Jingyang Zhong +2 more
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A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley +1 more source
A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Demonstratio Mathematica, 2016 We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2.
Laugier Alexandre, Saikia Manjil P.
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The k‐Augmented Pascal Matrix and Its Properties
Journal of Mathematics, Volume 2025, Issue 1, 2025.We define the k‐augmented Pascal matrix and present both a generalization and an alternative version of this matrix. We derive some properties of the defined matrices and establish a connection with generalized Stirling numbers and second‐order Eulerian numbers. Additionally, we provide a factorization of the k‐augmented Pascal matrix, highlighting its
Gonca Kizilaslan +2 more
wiley +1 more source
A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL
Journal of New Theory, 2017 The Fibonacci polynomial Fn(x) defined recurrently by Fn+1(x) = xFn(x)+Fn−1(x), with F0(x) = 0, F1(0) = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1(x) and Lbn+1(x) are introduced and
A. D. Godase, M. B. Dhakne
doaj
Some q-binomial identities involving the generalized q-Fibonacci numbers [PDF]
, 2018 In this paper, starting from the shifting property for the ordinary Fibonacci and q-Fibonacci numbers, we obtain some combinatorial identities involving the generalized Fibonacci and q-Fibonacci numbers of the first and second kind, and for the q ...
E. Munarini
core
p-Numerical Semigroups of Generalized Fibonacci Triples
, 2023 For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and the p-genus of generalized Fibonacci numerical semigroups. Here, the p-numerical semigroup Sp is defined as the set of integers whose nonnegative integral ...
Shanta Laishram +2 more
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Advances in Mathematical Physics, 2014 A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments.
Ayşe Betül Koç +2 more
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On Generalized Fibonacci Polynomials and Bernoulli Numbers
, 2005 In this paper we use elementary methods to study the relationship between the generalized Fibonacci polynomials and the famous Bernoulli numbers, and give several interesting identities involving ...
Yuankui Ma, Tianping Zhang
core
Fractal and FractionalThis study develops an effective numerical method for addressing the time-fractional gas dynamics equation formulated with the Caputo time-fractional derivative.
Waleed Mohamed Abd-Elhameed +5 more
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