Results 31 to 40 of about 847 (107)
On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
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Partitioning the positive integers with higher order recurrences
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 3, Page 457-462, 1991., 1991 Associated with any irrational number α > 1 and the function is an array {s(i, j)} of positive integers defined inductively as follows: s(1, 1) = 1, s(1, j) = g(s(1, j − 1)) for all j ≥ 2, s(i, 1) = the least positive integer not among s(h, j) for h ≤ i − 1 for i ≥ 2, and s(i, j) = g(s(i, j − 1)) for j ≥ 2.
Clark Kimberling
wiley +1 more source
Dynamical zeta functions and Kummer congruences [PDF]
, 2003 We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T such that the number of fixed points of the n-th iterate of T is equal to ...
de Reyna, J. Arias
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
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On r-Jacobsthal and r-Jacobsthal-Lucas Numbers
Annales Mathematicae Silesianae, 2023 Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences ...
Bilgici Göksal, Bród Dorota
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On the reciprocal sums of square of generalized bi-periodic Fibonacci numbers
, 2018 Recently Basbük and Yazlik [1] proved identities related to the reciprocal sum of generalized bi-periodic Fibonacci numbers starting from 0 and 1, and raised an open question whether we can obtain similar results for the reciprocal sum of mth power (m 2)
Ginkyu Choi, Y. Choo
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On Quaternion Gaussian Bronze Fibonacci Numbers
Annales Mathematicae Silesianae, 2022 In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
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On Cauchy Products of q−Central Delannoy Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this study, we have examined q− central Delannoy numbers and their Cauchy products. We have given some related equalities using the properties of recurrence relations.
Halıcı Serpil
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Simplifying Two Families of Nonlinear Ordinary Differential Equations
, 2017 In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.
Feng Qi (祁锋) +2 more
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