Results 61 to 70 of about 1,544,471 (165)
-Jacobsthal-Lucas hybrid numbers
, 2021 In this paper, we consider the k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. We obtain the Binet formulas, generating functions, exponential generating functions and summation formulas of k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Also, we
Nayil Kilic, KILIÇ, Nayil
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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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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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Some Special Identities for Jacobsthal and Jacobsthal-Lucas Generalized Octonions
, 2022 Summary: We study on Jacobsthal and Jacobsthal-Lucas generalized octonions over the algebra \(\mathbb{O}(a, b, c)\) where \(a\), \(b\) and \(c\) are real numbers. We present Binet formulas for these types of octonions.
Mert, Tuğba +3 more
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A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)
Journal of Advances in Mathematics and Computer Science, 2020 In this study, we bring into light a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as with initial conditions $$\ \hat{c}_{0}=2,\ \hat{c}_{1}=a.$$ The Binet formula as well as the generating function for this sequence are given. The convergence property of the consecutive
Evans Owusu, Sukran Uygun
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The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers
, 2021 In this paper, we regard the Padovan-p Jacobsthal sequence and then we discuss the connection of the Padovan-p Jacobsthal numbers and Jacobsthal numbers. Furthermore, we give the permanental, determinantal, combinatorial, and exponential representations,
Omur Deveci, Ozgur Erdag
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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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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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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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