Some Binomial Sums of \(\kappa\)-Jacobsthal and \(\kappa\)-Jacobsthal-Lucas Numbers

Authors

DOI:

https://doi.org/10.26713/cma.v14i1.1842

Keywords:

Jacobsthal number, Jacobsthal-Lucas number, κ-Jacobsthal number, κ-Jacobsthal-Lucas number

Abstract

In this paper, we formulate some crucial identities containing \(\kappa\)-Jacobsthal and \(\kappa\)-Jacobsthal-Lucas numbers and use these identities to establish some binomial sums of \(\kappa\)-Jacobsthal and \(\kappa\)-Jacobsthal-Lucas numbers.

Downloads

Download data is not yet available.

References

H. Campos, P. Catarino, A. P. Aires, P. Vasco and A. Borges, On some identities of k-JacobsthalLucas numbers, International Journal of Mathematical Analysis 8(10) (2014), 489 – 494, DOI: 10.12988/ijma.2014.4249.

L. Carlitz and H. Ferns, Some Fibonacci and Lucas identities, The Fibonacci Quarterly 8(1) (1970), 61 – 73, URL: https://www.fq.math.ca/Issues/8-1.pdf.

A. D. Godase, Binomial sums with k-Jacobsthal and k-Jacobsthal-Lucas numbers, Notes on Number Theory and Discrete Mathematics 28(3) (2022), 466 – 476, DOI: 10.7546/nntdm.2022.28.3.466-476.

A. F. Horadam, Jacobsthal representation numbers, The Fibonacci Quarterly 34(01) (1996), 40 – 54, URL: https://www.fq.math.ca/Scanned/34-1/horadam2.pdf.

D. Jhala, G. P. Rathore and K. Sisodiya, Some properties of k-Jacobsthal numbers with arithmetic indexes, Turkish Journal of Analysis and Number Theory 2(4) (2014), 119 – 124, DOI: 10.12691/tjant-2-4-3.

D. Jhala, G. P. Rathore and K. Sisodiya, On some identities for k-Jacobsthal numbers, International Journal of Mathematical Analysis 7(9-12) (2013), 551 – 556, DOI: 10.12988/ijma.2013.13052.

S. Srisawat, W. Sriprad and O. Sthityanak, On the k-Jacobsthal numbers by matrix methods, 2015 International Conference on Science and Technology (TICST), Pathum Thani, Thailand, 2015, pp. 445 – 448, DOI: 10.1109/ticst.2015.7369398.

S. Uygun, The (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences, Applied Mathematical Sciences 9(70) (2015), 3467 – 3476, DOI: 10.12988/ams.2015.52166.

S. Uygun and H. Eldogan, k-Jacobsthal and k-Jacobsthal Lucas matrix sequences, International Mathematical Forum 11(3) (2016), 145 – 154, DOI: 10.12988/imf.2016.51192.

S. Uygun and H. Eldogan, Properties of k-Jacobsthal and k-Jacobsthal Lucas sequences, General Mathematics Notes 36(1) (2016), 34 – 47.

S. Uygun and E. Owusu, A new generalization of Jacobsthal Lucas numbers (bi-periodic Jacobsthal Lucas sequence), Journal of Advances in Mathematics and Computer Science 34(5) (2020), 1 – 13, DOI: 10.9734/jamcs/2019/v34i530226.

S. Uygun and K. Uslu, The (s,t)-generalized Jacobsthal matrix sequences, In: Computational Analysis, Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, Volume 155) (2016), 325 – 336, DOI: 10.1007/978-3-319-28443-9_23.

Z. Zhang, Some identities involving generalized second-order integer sequences, The Fibonacci Quarterly 35(3) (1997), 265 – 267, URL: https://www.fq.math.ca/Scanned/35-3/zhang-zhizheng.pdf.

Downloads

Published

09-05-2023
CITATION

How to Cite

Godase, A. D. (2023). Some Binomial Sums of \(\kappa\)-Jacobsthal and \(\kappa\)-Jacobsthal-Lucas Numbers. Communications in Mathematics and Applications, 14(1), 143–152. https://doi.org/10.26713/cma.v14i1.1842

Issue

Vol. 14 No. 1 (2023)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.