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Journals / Sakarya University Journal of Science / 2026 / Volume: 25 Issue: 4

A New Approach to k-Jacobsthal Lucas Sequences

Hakan Akkuş(ERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0000-0001-9716-9424
Rabia Nagehan Üregen(ERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ)0000-0002-6824-4752
Engin Özkan(ERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ)0000-0002-4188-7248
Pages
—
Publication Date
2021-08-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined.
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Key Findings & Data:In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:k-Pell sequences · k-Lucas sequence · k-Fibonacci sequence

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.

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Cite This Article

Akkuş, H., Üregen, R. N., Özkan, E. (2021). A New Approach to k-Jacobsthal Lucas Sequences. Sakarya University Journal of Science, Volume: 25 Issue: 4. https://doi.org/10.16984/saufenbilder.842489

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References (16)

  1. Barry, P. 2005. ‘’A Catalan transform and related transformations on integer sequences’’. J.Integer Seq., 8(4), 1-24.
  2. Horadam, A. F. 1961. ‘’A generalized Fibonacci sequence’’. Amer. Math. Monthly, 68 (5), 455–459.
  3. Falcon, S. (2013). ‘’Catalan Transform of the k-Fibonacci sequence’’. Commun. Korean Math. Soc. 28(4), 827–832.
  4. Koshy, T. 2001. ‘’Fibonacci and Lucas Numbers with Applications’’. New York, NY: Wiley-Interscience Publication.
  5. Falc´on, S., and Plaza, A. 2007. ‘’On the Fibonacci k-numbers’’, Chaos Solitons Fractals 32(5), 1615–1624.
  6. Layman, J. W. 2001. ‘’The Hankel transform and some of its properties’’. J. Integer Seq. 4(1), 1-11.
  7. Bruhn, H. Gellert, L. Günther, J. 2015.‘’Jacobsthal numbers in generalized Petersen graphs’’ Electronic Notes in Discrete Mathematics, 49, 465-472.
  8. Anuradha, N. 2008. ‘’Number of points on certain hyperelliptic curves defined over finite fields’’ Finite Fields and Their Applications, 14, 314-328.
  9. Sloane, N. J. A., 2007. The on-line encyclopedia of integer sequences, www.research.att.com/˜njas/sequences/
  10. http://en.wikipedia.org/wiki/Catalan number
  11. 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.
  12. 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.
  13. Taştan, M.,Özkan, E. 2020. ‘’Catalan Transform of The k−Jacobsthal Sequence’’, Electronic Journal of Mathematical Analysis and Applications, 8(2), 70-74.
  14. 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.
  15. 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.
  16. 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.