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

The k-Jacobsthal sequence Jk,n, the k-Jacobsthal Lucas sequence jk,n, and the Binet like formula for them were described in this paper.

We investigate k-Jacobsthal and k Jacobsthal Lucas octonions over the algebra QR, where, and are real numbers, and then obtain Binet formulas for these octonins using the definitions of k-Jacobsthal Jk,n and k-Jacobsthal Lucas jk,n generalised octonions. Finally, we add the identities of Catalan, Cassini, and D'ocagne for these octonions.

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