On Hyperbolic Jacobsthal-Lucas Sequence

In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.

Keywords:

Hyperbolic numbers, Hyperbolic Jacobsthal-Lucas numbers Jacobsthal numbers,

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[1] A. F. Horadam, Jacobsthal represantation numbers, Fibonacci Quart., 34 (1996), 40-54.
[2] A. F. Horadam, Jacobsthal and Pell curves, Fibonacci Quart., 26 (1988), 79-83.
[3] A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart., 35 (1997), 137-148.
[4] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3) (1965), 161-176.
[5] K. Atanassov, Remark on Jacobsthal numbers, Part 2. Notes Number Theory Discrete Math., 17(2) (2011), 37-39.
[6] K. Atanassov, Short remarks on Jacobsthal numbers, Notes Number Theory Discrete Math., 18(2) (2012), 63-64.
[7] M. C. Dikmen, Hyperbolic Jacobsthal numbers, Asian Res. J. Math., 4 (2019), 1-9.
[8] S. Tas, The Hyperbolic Quadrapell sequences, Eastern Anatolian J. Sci. VII(I) (2021), 25-29.
[9] M. A. G¨ung¨or, A. Cihan, On dual-hyperbolic numbers with generalized Fibonacci and Lucas numbers components, Fundamental J. Math. App., 2(2) (2019), 162-172
[10] A. P. Stakhov, Gazale formulas, a new class of the hyperbolic Fibonacci and Lucas functions, and the improved method of the ’Golden’ Cryptograph, Academy of Trinitarism, 77(6567) (2006), 1–32.
[11] A. P. Stakhov, I. S. Rozin, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9–14, [In Russian].
[12] A. P. Stakhov, B. Tkachenko, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379–389.
[13] F. Falcon, A. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38(2) (2008), 409–420.
[14] F. T. Aydın, Hyperbolic Fibonacci sequence, Univers. J. Math. Appl., 2(2) (2019), 59-64.
[15] S. Halıcı, On bicomplex Jacobsthal-Lucas numbers, J. Math. Sci. Model., 3(3) (2020), 139-143.
[16] H. Gargoubi, S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebras, 26(4) (2016), 1211-1233.
[17] A. E. Motter, A. F. Rosa, Hyperbolic calculus, Adv. App. Clifford Algebras, 8(1) (1998), 109-128.
[18] L. Barreira, L. H. Popescu, C. Valls, Hyperbolic sequences of linear operators and evolution maps, Milan J. Math., 84 (2016), 203-216.