k-JACOBSTHAL AND k-JACOBSTHAL-LUCAS GENERALIZED OCTONIONS

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.