On Third Order Hyperbolic Jacobsthal Numbers

Year 2022, Volume: 10 Issue: 1, 118 - 126, 15.04.2022

Can Murat Dikmen , Mustafa Altınsoy

Abstract

In this paper, we introduce the hyperbolic third order Jacobsthal and Jacobsthal-Lucas numbers and we present recurrence relations, Binet's formulas, generating functions and the summation formulas for these numbers.

Keywords

Third order Jacobsthal numbers , third order Jacobsthal-Lucas numbers numbers , third order hyperbolic Jacobsthal numbers , third order hyperbolic Jacobsthal-Lucas numbers

References

• [1] Horadam, A. F. “Jacobsthal Representation Numbers.” Fib. Quart. 34, 40-54, 1996.
• [2] Sobczyk, G.. The Hyperbolic Number Plane, The College Mathematics Journal, 26(4), (1995) 268–280.
• [3] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
• [4] F. Torunbalcı Aydın, On generalisations of the Jacobsthal Sequence, Notes on Number Theory and Discrete Mathematics, Online ISSN
• [5] F. Torunbalcı Aydın, Hyperbolic Fibonacci Sequence, Universal Journal of Mathematics and Applications, Cilt 2, Sayı 2, (2019), 59-62.
• [6] Y.Soykan, On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints (2019), 2019100172 (doi: 10.20944/preprints201910.0172.v1).
• [7] Y. Soykan, ve M. G¨ocen, Properties of hyperbolic generalized Pell numbers. Notes on Number Theory and Discrete Mathematics,Vol. 26, (2020), No. 4, 136–153.
• [8] C. M. Dikmen, Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, 15 (4) (2019), 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
• [9] Tas¸yurdu Y. Hyperbolic Tribonacci and Tribonacci-Lucas Sequences, International Journal of Mathematical Analysis Vol. 13, 2019, no. 12, 565 - 572 https://doi.org/10.12988/ijma.2019.91167
• [10] G. Cerda -Morales, Identities for Third Order Jacobsthal Quaternions, Advances in AppliedCifford Algebras 27(2) (2017), 1043-1053.
• [11] G. Cerda -Morales, A Note On Dual Third Order Jacobsthal Vectors, Preprints 2017, arXiv:1712.08950v1[math.RA]
• [12] Charles K. Cook and Michael R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae, 41 (2013) pp. 27–39.