Research Article
BibTex RIS Cite
Year 2021, Issue: 34, 12 - 19, 30.03.2021

Abstract

References

  • K. S. Williams, The nth Power of a 2×2 Matrix, Mathematics Magazine 65(5) (1992) 336-336.
  • J. Mc Laughlin, Combinatorial Identities Deriving from the nth Power of a 2×2 Matrix, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004) 1-15.
  • J. Mc Laughlin, B. Sury, Powers of Matrix and Combinatorial Identities, Integers: Electronic Journal of Combinatorial Number Theory 5 (2005) 1-9.
  • H. Belbachir, Linear Recurrent Sequences and Powers of a Square Matrix, Integers: Electronic Journal of Combinatorial Number Theory 6 (2006) 1-17.
  • G. E. Bergum, V. E. Hoggatt Jr., Sums and products for recurring sequences, The Fibonacci Quarterly, 13(2) (1975) 115-120.
  • Z. Akyüz, S. Halıcı, On Some Combinatorial Identities Involving the Terms of Generalized Fibonacci and Lucas Sequences, Hacettepe Journal of Mathematics and Statistics 42(4) (2013) 431-435.
  • Z. Akyüz, S. Halıcı, Some Identities Deriving from the nth Power of a Special Matrix. Advances in Difference Equations 1 (2012) 1-6.
  • S. Uygun, The (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas Sequences, Applied Mathematical Sciences 70(9) (2015) 3467-3476.
  • K. Uslu, S. Uygun, The (s,t)-Jacobsthal and (s,t)-Jacobsthal-Lucas Matrix Sequences, ARS Combinatoria 108 (2013) 13-22.
  • S. Uygun, Some Sum Formulas of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas Matrix Sequences, Applied Mathematics 7 (2016) 61-69.
  • S. Halıcı, M. Uysal, A Study on Some identities involving (s_k,t)-Jacobsthal Numbers, Notes on Number Theory and Discrete Mathematics 26(4) (2020) 4 74-79. DOI: 10.7546/nntdm.2020.26.4.74-79
  • A. A. Wani, P. Catarino, S. Halıcı, On a Study of (s,t)-generalized Pell Sequence and Its Matrix Sequence, Journal of Mathematics 51(9) (2019) 17-32.
  • A. F. Horadam, Jacobsthal Representation Numbers, The Fibonacci Quarterly 34(1) (1996) 40-54.

The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties

Year 2021, Issue: 34, 12 - 19, 30.03.2021

Abstract

In this study, new formulas for the nth power of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas special matrix sequences are established by using determinant and trace of the matrices. By these formulas, some identities for (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences are obtained. The formulas for finding the nth power for classic Jacobsthal and Jacobsthal Lucas matrix sequences are also derivable if we choose s=t=1.

References

  • K. S. Williams, The nth Power of a 2×2 Matrix, Mathematics Magazine 65(5) (1992) 336-336.
  • J. Mc Laughlin, Combinatorial Identities Deriving from the nth Power of a 2×2 Matrix, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004) 1-15.
  • J. Mc Laughlin, B. Sury, Powers of Matrix and Combinatorial Identities, Integers: Electronic Journal of Combinatorial Number Theory 5 (2005) 1-9.
  • H. Belbachir, Linear Recurrent Sequences and Powers of a Square Matrix, Integers: Electronic Journal of Combinatorial Number Theory 6 (2006) 1-17.
  • G. E. Bergum, V. E. Hoggatt Jr., Sums and products for recurring sequences, The Fibonacci Quarterly, 13(2) (1975) 115-120.
  • Z. Akyüz, S. Halıcı, On Some Combinatorial Identities Involving the Terms of Generalized Fibonacci and Lucas Sequences, Hacettepe Journal of Mathematics and Statistics 42(4) (2013) 431-435.
  • Z. Akyüz, S. Halıcı, Some Identities Deriving from the nth Power of a Special Matrix. Advances in Difference Equations 1 (2012) 1-6.
  • S. Uygun, The (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas Sequences, Applied Mathematical Sciences 70(9) (2015) 3467-3476.
  • K. Uslu, S. Uygun, The (s,t)-Jacobsthal and (s,t)-Jacobsthal-Lucas Matrix Sequences, ARS Combinatoria 108 (2013) 13-22.
  • S. Uygun, Some Sum Formulas of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas Matrix Sequences, Applied Mathematics 7 (2016) 61-69.
  • S. Halıcı, M. Uysal, A Study on Some identities involving (s_k,t)-Jacobsthal Numbers, Notes on Number Theory and Discrete Mathematics 26(4) (2020) 4 74-79. DOI: 10.7546/nntdm.2020.26.4.74-79
  • A. A. Wani, P. Catarino, S. Halıcı, On a Study of (s,t)-generalized Pell Sequence and Its Matrix Sequence, Journal of Mathematics 51(9) (2019) 17-32.
  • A. F. Horadam, Jacobsthal Representation Numbers, The Fibonacci Quarterly 34(1) (1996) 40-54.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şükran Uygun 0000-0002-7878-2175

Publication Date March 30, 2021
Submission Date April 15, 2019
Published in Issue Year 2021 Issue: 34

Cite

APA Uygun, Ş. (2021). The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties. Journal of New Theory(34), 12-19.
AMA Uygun Ş. The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties. JNT. March 2021;(34):12-19.
Chicago Uygun, Şükran. “The Nth Power of Generalized (s, T)-Jacobsthal and (s, T)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties”. Journal of New Theory, no. 34 (March 2021): 12-19.
EndNote Uygun Ş (March 1, 2021) The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties. Journal of New Theory 34 12–19.
IEEE Ş. Uygun, “The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties”, JNT, no. 34, pp. 12–19, March 2021.
ISNAD Uygun, Şükran. “The Nth Power of Generalized (s, T)-Jacobsthal and (s, T)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties”. Journal of New Theory 34 (March 2021), 12-19.
JAMA Uygun Ş. The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties. JNT. 2021;:12–19.
MLA Uygun, Şükran. “The Nth Power of Generalized (s, T)-Jacobsthal and (s, T)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties”. Journal of New Theory, no. 34, 2021, pp. 12-19.
Vancouver Uygun Ş. The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties. JNT. 2021(34):12-9.


TR Dizin 26024

Electronic Journals Library (EZB) 13651



Academindex 28993

SOBİAD 30256                                                   

Scilit 20865                                                  


29324 As of 2021, JNT is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).