TY - JOUR T1 - On Pell and Pell-Lucas Generalized Octonions AU - Mert, Tuğba AU - Tokeşer, Ümit AU - Ünal, Zafer AU - Bilgici, Göksal PY - 2021 DA - December DO - 10.47000/tjmcs.780474 JF - Turkish Journal of Mathematics and Computer Science JO - TJMCS PB - Matematikçiler Derneği WT - DergiPark SN - 2148-1830 SP - 226 EP - 233 VL - 13 IS - 2 LA - en AB - In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ and $c$ are real numbers. For these number sequences, we obtain Binet formulas and gave some well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity. KW - Generalized octonion KW - Pell octonion KW - Pell-Lucas octonion CR - [1] Akkus, I., Kecilioglu, O., Split Fibonacci and Lucas Octonions, Adv. Appl. Clifford Algebras, 25(2015), 517–525. CR - [2] Akyiğit, M., Kösal, H.H., Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24(2014), 631–641. CR - [3] Catarino, P., The Modified Pell and The Modified k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebras, 26(2)(2016), 577–590. CR - [4] Cimen, C.B., İpek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebras, 26(2016), 39–51. CR - [5] Flaut, C., Stefanescu, M., Some Equations over Generalized Quaternion and Octonion Division Algebras, Bull. Math. Soc. Sci. Math. Roum., 52(100)(4)(2009), 427–439. CR - [6] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327. CR - [7] Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70(1963), 289–291. CR - [8] Horadam, A.F., Quaternion Recurrence Relations, Ulam Quarterly, 2(1993), 23–33. CR - [9] Iakin, A.L., Generalized Quaternions of Higher Order, Fibonacci Quart, 15(1977), 343–346. CR - [10] Iyer, M.R., A Note on Fibonacci Quaternions, Fibonacci Quart, 3(1969), 225–229. CR - [11] Keçilioğlu, O., Akkus, I., The Fibonacci Octonions, Adv. Appl. Clifford Algebras, 25(2015), 151–158. CR - [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001. CR - [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014. CR - [14] Ramirez, J.L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta, 23(2)(2015), 201–212. CR - [15] Savin, D., Some Properties of Fibonacci numbers, Fibonacci Octonions, and generalized Fibonacci-Lucas Octonions, Adv. Difference Equ., 2015.1(2015), 298. CR - [16] Swamy, M.N.S., On Generalized Fibonacci Quaternions, The Fib. Quarterly, 5(1973), 547–550. CR - [17] Szynal-Liana, A., Wloch, I., The Pell Quaternions and The Pell Octonions, Adv. Appl. Clifford Algebras, 26(2016), 435–440 UR - https://doi.org/10.47000/tjmcs.780474 L1 - https://dergipark.org.tr/en/download/article-file/1240332 ER -