Results 51 to 60 of about 1,634,732 (135)
On a two-parameter generalization of Jacobsthal numbers and its graph interpretation [PDF]
, 2018 In this paper we introduce a two-parameter generalization of the classical Jacobsthal numbers ((s,p)-Jacobsthal numbers). We present some properties of the presented sequence, among others Binet’s formula, Cassini’s identity, the generating function ...
Bród, Dorota
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On Hyperbolic Jacobsthal-Lucas Sequence
Fundamental Journal of Mathematics and Applications, 2022 In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.
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Qualitative Behavior of Bidimensional Rational Fuzzy Difference Equations
Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.This paper aims to extend the research conducted by Yalçınkaya et al. on one‐dimensional dynamics, specifically, their work titled “Qualitative behavior of a higher‐order fuzzy difference equation.” The purpose of this study is to expand the analysis of fuzzy difference equations into a bidimensional framework.
Najmeddine Attia +2 more
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Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.
Yanpeng Zheng, Sugoog Shon, Zidong Wang
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A note on Modified Third-order Jacobsthal Numbers
, 2020 Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.Modified third-order Jacobsthal sequence is defined in this study.
Cerda-Morales, Gamaliel
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Journal of Mathematics, Volume 2024, Issue 1, 2024.Spinors can be expressed as Lie algebra of infinitesimal rotations. Spinors are also defined as elements of a vector space which carries a linear representation of the Clifford algebra typically. The motivation for this study is to define a new and particular sequence.
Tülay Erişir, Serkan Araci
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Jacobsthal-Lucas series and their applications [PDF]
, 2017 In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence. In particular, we consider the properties of the set of incomplete sums as well as their applications.
Karvatsky, D., Pratsiovytyi, M.
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Some infinite series summations involving linear recurrence relations of order 2 and 3 [PDF]
Notes on Number Theory and Discrete MathematicsThis paper extends known results of second and third order recursive sequences through extensive formulations of properties of the roots of their characteristic equations, some are old but most are new. They are applied to novel studies of Σₙ₌ₒ^∞ aₘₙ/10ⁿ⁺
Anthony G. Shannon +4 more
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A New Approach to k-Jacobsthal Lucas Sequences
Sakarya University Journal of Science, 2021 In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined. S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas S_(k,n) sequences is obtained.In addition the transformation of CS_(k,n) is written as the product of the Catalan matrix C, which is the lower triangular matrix, and the S_k matrix of type 𝑛 𝑥 1 ...
Hakan AKKUŞ +2 more
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The Jacobsthal and Jacobsthal-Lucas sequences associated with pseudo graphs
, 2012 In the present paper, we define two directed pseudo graphs. Then, we investigate the adjacency matrices of the defined graphs and show that the permanents of the adjacency matrices are Jacobsthal and Jacobsthal-Lucas numbers.
Yılmaz, Fatih, Bozkurt, Durmuş
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