Results 21 to 30 of about 1,634,732 (135)
The Complex‐Type k‐Pell Numbers and Their Applications
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In this study, a new sequence called the complex‐type k‐Pell number is defined. Also, we give properties of this sequence such as the generating matrix, the generating function, the combinatorial representations, the exponential representation, the sums, the permanental and determinantal representations, and the Binet formula.
Yeşim Aküzüm, Xiaogang Liu
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The arrowhead-Jacobsthal sequence
Mathematica Montisnigri, 2021 In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix.
Yesım Akuzum, Omur Deveci
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Solutions of the Diophantine Equations Br = Js + Jt and Cr = Js + Jt
Journal of Mathematics, Volume 2023, Issue 1, 2023., 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. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella
Ahmed Gaber +2 more
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On the properties of Generalized Jacobsthal and Generalized Jacobsthal-Lucas sequences
WSEAS TRANSACTIONS ON MATHEMATICS, 2023 In this paper, we study the Generalized Jacobsthal and Generalized Jacobsthal-Lucas sequences. We also present some properties on relationship between the Generalized Jacobsthal sequence and Generalized Jacobsthal-Lucas sequence by using Binet’s formula for derivation.
Sukanya Somprom +2 more
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Coprime mappings and lonely runners
Mathematika, Volume 68, Issue 3, Page 784-804, July 2022., 2022 Abstract For x real, let {x}$ \lbrace x \rbrace$ be the fractional part of x (that is, {x}=x−⌊x⌋$\lbrace x\rbrace = x - \lfloor x \rfloor$). The lonely runner conjecture can be stated as follows: for any n positive integers v1
Tom Bohman, Fei Peng
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Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
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On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions [PDF]
, 2022 summary:We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and ...
Bród, Dorota +2 more
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Catalan Transform of k‐Balancing Sequences
International Journal of Mathematics and Mathematical Sciences, Volume 2021, Issue 1, 2021., 2021 In this work, the Catalan transformation (CT) of k‐balancing sequences, Bk,nn≥0, is introduced. Furthermore, the obtained Catalan transformation CBk,nn≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k‐balancing sequences, Bk,nn≥0, which is an n × 1 matrix.
Asim Patra +2 more
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Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
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On fourth-order jacobsthal quaternions
Journal of Mathematical Sciences and Modelling, 2018 In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
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