Results 1 to 10 of about 267 (124)

Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt

Journal of Mathematics, 2023
Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
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On Some Properties of Bihyperbolic Numbers of The Lucas Type

Communications in Advanced Mathematical Sciences, 2023
To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
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On Fibonacci (k,p)-Numbers and Their Interpretations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to
Berke Cengiz, Yasemin Taşyurdu
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On complex gaussian jacobsthal and jacobsthal-lucas quaternions

Cumhuriyet Science Journal, 2020
The main aim of this work is to introduce the complex Gaussian Jacobsthal and Jacobsthal-Lucas quaternions and investigate their structures. We obtain the recurrence relations, Binet formulas and generating functions for these quaternions.
Hasan Arslan
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GENERATING FUNCTIONS OF THE PRODUCT OF 2-ORTHOGONAL CHEBYSHEV POLYNOMIALS WITH SOME NUMBERS AND THE OTHER CHEBYSHEV POLYNOMIALS

Проблемы анализа, 2020
In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions

Axioms, 2023
In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
Takao Komatsu, Claudio Pita-Ruiz
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On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
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The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation

Journal of Applied Mathematics, 2012
Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph.
Fatih Yılmaz, Durmuş Bozkurt
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Some bounds for the spectral norms of some circulant matrices with generalized Jacobsthal–Lucas numbers

Mathematics Open
The purpose of this paper is to investigate the bounds of the spectral norms of some circulant matrices whose elements are a generalization of Jacobsthal–Lucas numbers called bi-periodic Jacobsthal–Lucas numbers by three different ways.
Sukran Uygun
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Generalized commutative Jacobsthal quaternions and some matrices

Examples and Counterexamples, 2023
In this paper, some examples of matrix generators for generalized commutative Jacobsthal quaternions were given. The generating matrices are useful tools for the number sequences satisfying a recurrence relation.
Dorota Bród, Anetta Szynal-Liana
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