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Year 2021, Volume: 25 Issue: 4, 969 - 973, 30.08.2021

Hakan Akkuş Rabia Nagehan Üregen Engin Özkan

https://doi.org/10.16984/saufenbilder.842489
Cited By: 3

Abstract

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.

A New Approach to k-Jacobsthal Lucas Sequences

Year 2021, Volume: 25 Issue: 4, 969 - 973, 30.08.2021

Hakan Akkuş Rabia Nagehan Üregen Engin Özkan

https://doi.org/10.16984/saufenbilder.842489
Cited By: 3

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.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hakan Akkuş 0000-0001-9716-9424

Rabia Nagehan Üregen 0000-0002-6824-4752

Engin Özkan 0000-0002-4188-7248

Publication Date August 30, 2021
Submission Date March 1, 2021
Acceptance Date June 24, 2021
Published in Issue Year 2021 Volume: 25 Issue: 4

Cite

APA Akkuş, H., Üregen, R. N., & Özkan, E. (2021). A New Approach to k-Jacobsthal Lucas Sequences. Sakarya University Journal of Science, 25(4), 969-973. https://doi.org/10.16984/saufenbilder.842489
AMA Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. August 2021;25(4):969-973. doi:10.16984/saufenbilder.842489
Chicago Akkuş, Hakan, Rabia Nagehan Üregen, and Engin Özkan. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science 25, no. 4 (August 2021): 969-73. https://doi.org/10.16984/saufenbilder.842489.
EndNote Akkuş H, Üregen RN, Özkan E (August 1, 2021) A New Approach to k-Jacobsthal Lucas Sequences. Sakarya University Journal of Science 25 4 969–973.
IEEE H. Akkuş, R. N. Üregen, and E. Özkan, “A New Approach to k-Jacobsthal Lucas Sequences”, SAUJS, vol. 25, no. 4, pp. 969–973, 2021, doi: 10.16984/saufenbilder.842489.
ISNAD Akkuş, Hakan et al. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science 25/4 (August 2021), 969-973. https://doi.org/10.16984/saufenbilder.842489.
JAMA Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. 2021;25:969–973.
MLA Akkuş, Hakan et al. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science, vol. 25, no. 4, 2021, pp. 969-73, doi:10.16984/saufenbilder.842489.
Vancouver Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. 2021;25(4):969-73.

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