k-Jacobsthal and k-Jacobsthal Lucas matrix sequences

Abstract

In this study, we consider sequences named k-Jacobsthal, k-Jacobsthal Lucas sequences. After that, by using these sequences, we define k-Jacobsthal and k-Jacobsthal-Lucas matrix sequence at the same time. Finally we investigate some properties of these sequences, present some important relationship between k-Jacobsthal matrix sequence and k-Jacobsthal Lucas matrix sequence.

Generalized a:k:m-Fibonacci Numbers

“…The k-Fibonacci numbers introduced by Falcon and Plaza [9] and seriously studied by other researchers [10][11][12][13][14][15][16][17][18][19][20][21][22][23] are defined by…”

On hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions

“…In 2016, Uygun and Eldogan [22] defined k-Jacobsthal numbers by the recurrence relation The quaternion, an algebraic structure, was first described in 1843 by William Rowan Hamilton [11].…”

Hyperbolic $$\pmb k$$-Jacobsthal and $$\pmb k$$-Jacobsthal-Lucas Quaternions

“…Binet formula of Jacobsthal-Lucas numbers j n j n = a + b with a = 2 and b = 1 are the roots of the characteristic equation x 2 − x − 2 = 0. Uygun and Eldogan [2] defined the k− Jacobsthal numbers by the recurrence relation…”

“…are the roots of the characteristic equation x 2 − kx − 2 = 0. Uygun and Eldogan [2] defined k− Jacobsthal-Lucas numbers by the recurrence relation…”