Results 51 to 60 of about 122 (113)
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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Total Graph Interpretation of the Numbers of the Fibonacci Type
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give the lower bound and the upper bound for the number of all (A1, 2A1)‐edge colourings in trees.
Urszula Bednarz +3 more
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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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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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A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order f(x) = pf(x − 1) + qf(x − 2) + rf(x − 3), which is strongly associated with a well‐known identity for the Fibonacci numbers. Moreover, we prove the Hyers‐Ulam stability of that equation.
Soon-Mo Jung +2 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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Determinant Representations of Sequences: A Survey
Special Matrices, 2014 This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices.
Moghaddamfar A. R. +2 more
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Relations Established Between Hypergeometric Functions and Some Special Number Sequences
AxiomsIn this paper, we establish new hypergeometric representations for two classical integer sequences, namely the Pell and Jacobsthal sequences. Motivated by Dilcher’s hypergeometric formulations of the Fibonacci sequence, we extend this framework to other ...
Sukran Uygun, Berna Aksu, Hulya Aytar
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On the Lagrange Interpolations of the Jacobsthal and Jacobsthal-Lucas Sequences
Journal of Universal MathematicsThis study explores the formation of polynomials of at most degree $n$ using the first $n+1$ terms of the Jacobsthal and Jacobsthal-Lucas sequences through Lagrange interpolation. The paper provides a detailed examination of the recurrence relations and various identities associated with the Jacobsthal and Jacobsthal-Lucas Lagrange Interpolation ...
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