A New Approach to k-Jacobsthal Lucas Sequences

Abstract

In this study, Catalan transformation 𝐶𝑆 𝑘,𝑛 of 𝑘−Jacobsthal-Lucas sequences 𝑆 𝑘,𝑛 is defined. 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, and the Hankel transformations of some 𝑘−Jacobsthal-Lucas numbers is found.

Special transforms of the generalized bivariate Fibonacci and Lucas polynomials

“…• If we replace p = 1, q = 2k in CK n (ξ, ς), HCK n (ξ, ς), we obtain the Catalan, Hankel transforms for k-Jacobsthal-Lucas numbers in [1]. • If we replace p = k, q = 1 in CH n (ξ, ς), HCH n (ξ, ς), b n (ξ, ς) , we obtain the Catalan, Hankel, binomial transforms for k-Fibonacci numbers in [7,8].…”

Applications of Jacobsthal and Jacobsthal-Lucas numbers in coding theory

“…Coding theory has been studied by many authors with different number sequences [3][4][5][6]. In particular, the Fibonacci and Lucas sequences and their more general versions, the Fibonacci and Lucas p-number sequences, have been studied [7][8][9][10][11][12][13].…”