Full Article - PDF

Published: 2021-04-01

Page: 1-6


Department of Mathematics, Faculty of Science, Bengazi University, Libya.


Department of Mathematics, Faculty of Sciene and Arts, Kastamonu University, Turkey.

*Author to whom correspondence should be addressed.


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

How to Cite

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://ikprress.org/index.php/AJOMCOR/article/view/6151


Download data is not yet available.


Ram˙Irez Jose L. Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions. Analele Universitati” Ovidius” Constanta-Seria Matematica. 2015;23(2):201-212.

Uygun ¸s, Eldogan H. k-Jacobsthal and k-Jacobsthal Lucas matrix sequences. In Int. Math. Forum. 2016;11:145-154.

Bilgici, G¨oksal; Toka¸ser, Umit; ¨ Unal, Zafer. ¨ k-fibonacci and k-lucas generalized quaternions. Konuralp Journal of Mathematics. 2017; 5(2):102-113.

Jhala, Deepika, Sisodiya, Kiran, Rathore, GPS. On some identities for k-Jacobsthal numbers. Int. J. Math. Anal. (Ruse). 2013;7.9-12:551-556.

Uygun, S¸.; Eldogan, H. Properties of k-Jacobsthal and k-Jacobsthal Lucas sequences. General Mathematics Notes. 2016;36(1):34.

Uygun, Sukran, Owusu, Evans. A new generalization of Jacobsthal numbers (bi-periodic Jacobsthal sequences). Journal of Mathematical Analysis. 2016;7(5):28-39.

Tasci, Dursun. On k-Jacobsthal and k-Jacobsthal-Lucas quaternions. Journal of Science and Arts. 2017;17(3):469-476.

Yasarsoy, Sevda, Acikgoz Mehmet, Duran Ugur. A Study on the k-Jacobsthal and k-Jacobsthal Lucas Quaternions and Octonions.

C¸imen, Cennet Bolat; ˙Ipek, Ahmet. On jacobsthal and jacobsthal lucas octonions. Mediterranean Journal of Mathematics. 2017;14:37.

Bilgici G¨oksal, et al. On Fibonacci and Lucas generalized octonions; 2018.

Savin, Diana. Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions. Advances in Difference Equations. 2015;2015(1):1-10.

Karata S¸, Adnan, Halici, Serpil. Horadam octonions. Analele Universitatii” Ovidius” Constanta-Seria Matematica. 2017;25(3):97-106.