A New Approach to k-Jacobsthal Lucas Sequences

Year 2021, , 969 - 973, 30.08.2021

Hakan Akkuş , Rabia Nagehan Üregen , Engin Özkan

https://doi.org/10.16984/saufenbilder.842489

Cited By: 4

Abstract

In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined. S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas S_(k,n) sequences is obtained.In addition the transformation of CS_(k,n) is written as the product of the Catalan matrix C, which is the lower triangular matrix, and the S_k matrix of type 𝑛 𝑥 1, and the Hankel transformations of some k-Jacobsthal-Lucas numbers has been found.

Keywords

k-Pell sequences, k-Lucas sequence, k-Fibonacci sequence, Catalan Transform, Hankel Transform

References

• Barry, P. 2005. ‘’A Catalan transform and related transformations on integer sequences’’. J.Integer Seq., 8(4), 1-24.
• Horadam, A. F. 1961. ‘’A generalized Fibonacci sequence’’. Amer. Math. Monthly, 68 (5), 455–459.
• Falcon, S. (2013). ‘’Catalan Transform of the k-Fibonacci sequence’’. Commun. Korean Math. Soc. 28(4), 827–832.
• Koshy, T. 2001. ‘’Fibonacci and Lucas Numbers with Applications’’. New York, NY: Wiley-Interscience Publication.
• Falc´on, S., and Plaza, A. 2007. ‘’On the Fibonacci k-numbers’’, Chaos Solitons Fractals 32(5), 1615–1624.
• Layman, J. W. 2001. ‘’The Hankel transform and some of its properties’’. J. Integer Seq. 4(1), 1-11.
• Bruhn, H. Gellert, L. Günther, J. 2015.‘’Jacobsthal numbers in generalized Petersen graphs’’ Electronic Notes in Discrete Mathematics, 49, 465-472.
• Anuradha, N. 2008. ‘’Number of points on certain hyperelliptic curves defined over finite fields’’ Finite Fields and Their Applications, 14, 314-328.
• Sloane, N. J. A., 2007. The on-line encyclopedia of integer sequences, www.research.att.com/˜njas/sequences/
• http://en.wikipedia.org/wiki/Catalan number
• Boussayoud, A., Kerada, M. and , Harrouche, N. 2017. ‘’On the k -Lucas Numbers and Lucas Polynomials’’, Turkish Journal of Analysis and Number Theory, 5(4), 121-125.
• Özkan E., Altun İ., Göçer A. 2017, "On Relationship Among A New Family of k-Fibonacci, k-Lucas Numbers, Fibonacci And Lucas Numbers", Chiang Mai Journal of Scıence, 44, 1744-1750.
• Taştan, M.,Özkan, E. 2020. ‘’Catalan Transform of The k−Jacobsthal Sequence’’, Electronic Journal of Mathematical Analysis and Applications, 8(2), 70-74.
• Özkan, E., Taştan, M., Aydoğdu, A. 2019. ‘’3-Fibonacci Polynomials in The Family of Fibonacci Numbers’’, Erzincan University Journal of the Institute of Science and Technology, 12(2), 926-933.
• Rajkovi´c, P. M., Petkovi´c, M. D. and Barry, P. 2007. ‘’The Hankel transform of the sum of consecutive generalized Catalan numbers. Integral Transforms Spec. Funct’’. 18(4), 285–296.