The relations between bi-periodic jacobsthal and bi-periodic jacobsthal lucas sequence

Abstract

In this paper, one of the special integer sequences, Jacobsthal and Jacobsthal Lucas sequences which are encountered in computer science is generalized according to parity of the index of the entries of the sequences, called bi-periodic Jacobsthal and Jacobsthal Lucas sequences. The definitions of the bi-periodic Jacobsthal and Jacobsthal Lucas sequences are given by using classic Jacobsthal and Jacobsthal Lucas sequences. In literature, there were some relations for the bi-periodic Jacobsthal and Jacobsthal Lucas sequences. We find new identities for these sequences. If we substitute 𝑎 = 𝑏 = 1 in the results, we get identities for classic Jacobsthal and Jacobsthal Lucas sequences.