k-JACOBSTHAL AND k-JACOBSTHAL-LUCAS GENERALIZED OCTONIONS
RAGEA AHMED BOHAGR *
Department of Mathematics, Faculty of Science, Bengazi University, Libya.
UMIT TOKESER
Department of Mathematics, Faculty of Sciene and Arts, Kastamonu University, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper we defined the k-Jacobsthal sequence {Jk,n}, the k-Jacobsthal-Lucas sequence {jk,n} and the Binet like formula of them. We study on k-Jacobsthal and k-Jacobsthal Lucas octonions over the algebra QR where the α, β and γ are real numbers, after that by definition of k-Jacobsthal {Jˆk,n} and k-Jacobsthal Lucas {ˆjk,n} generalized octonions we obtain Binet formulas for these octonins. Finally, for these octonions we introduce Catalan’s identity, Cassini’s identity and D’ocagne’s identity.
Keywords: kJacobsthal numbers, kJacobsthal Lucas numbers, Generalized octonion, Genrating function, k-Jacobsthal octonion, k-Jacobsthal Lucas octonion