k-JACOBSTHAL AND k-JACOBSTHAL-LUCAS GENERALIZED OCTONIONS | Asian Journal of Mathematics

The k-Jacobsthal sequence Jk,n, the k-Jacobsthal-Lucas sequence jk,n, and the Binet like formula for them were defined in this study. We investigate k-Jacobsthal and k-Jacobsthal Lucas octonions over the algebra QR, where, and are real numbers, and then establish Binet formulas for these octonins using the definitions of k-Jacobsthal Jk,n and k-Jacobsthal Lucas jk,n generalised octonions. Finally, we introduce the identities of Catalan, Cassini, and D'ocagne for these octonions.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/6151