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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. 

kJacobsthal numbers, kJacobsthal Lucas numbers, Generalized octonion, Genrating function, k-Jacobsthal octonion, k-Jacobsthal Lucas octonion

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BOHAGR, R. A., & TOKESER, U. (2021). k-JACOBSTHAL AND k-JACOBSTHAL-LUCAS GENERALIZED OCTONIONS. Asian Journal of Mathematics and Computer Research, 28(1), 1-6. Retrieved from https://www.ikprress.org/index.php/AJOMCOR/article/view/6151
Original Research Article


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