Matrix Representation of Bi-Periodic Pell Sequence

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science and Arts, Gaziantep University, Gaziantep, Turkiye

Abstract

In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers. Then the generating function, Binet formula and some basic properties and sum formulas are examined.

Keywords

References

[1] A. Coskun, N. Taskara, A note on the bi-periodic Fibonacci and Lucas matrix sequences, Applied Mathematics and Computation vol.320 (2018) 400{406.
[2] A. F. Horadam, B. J. M. Mahon, Pell and Pell Lucas Polynomials, The Fibonacci Quarterly vol.23, no.1 (1985) 7{20.
[3] G. Bilgici, Two generalizations of Lucas sequence, Applied Mathematics and Computation vol.245 (2014) 526{538.
[4] M. Edson, O. Yayenie, A new generalization of Fibonacci sequences and the extended Binet's formula, INTEGERS Electron. J. Comb. Number Theory vol.9 (2009) 639{654.
[5] M. Tastan, E. Ozkan, Catalan transform of the k􀀀Pell, k􀀀Pell{Lucas and modi ed k􀀀Pell sequence, Notes on Number Theory and Discrete Mathematics vol.27, no.1 (2021) 198{207.
[6] N. Yilmaz, A. Aydogdu, E. Ozkan, Some Properties of k􀀀Generalized Fibonacci Numbers, Mathematica Montisnigri vol.L (2021) 73{79.
[7] O. Yayenie, A note on generalized Fibonacci sequence, Appl. Math. Comput. vol.217 (2011) 5603{5611.
[8] S. Celik, I. Durukan, E. Ozkan, New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal Lucas numbers, Chaos, Solitons & Fractals vol.150, no.111173 (2021) 1{8.
[9] S. Uygun, E. Owusu, A New Generalization of Jacobsthal Numbers (Bi-Periodic Jacob-sthal Sequences), Journal of Mathematical Analysis vol.7, no.5 (2016) 28{39.
[10] S. Uygun, H. Karatas, A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence), Communications in Mathematics and Applications vol.10, no.3 (2019) 1{12.
[11] S. Uygun, H. Karatas, Bi-Periodic Pell Sequence, Academic Journal of Applied Mathematical Sciences vol.6, no.7 (2020) 136{144.
[12] S. Uygun, E. Owusu, Matrix Representation of bi-Periodic Jacobsthal Sequence, Journal of Advances in Mathematics and Computer Science vol.34, no.6 (2020) 1{12.
[13] S. Uygun, E. Owusu, A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence), Journal of Advances in Mathematics and Computer Science vol.34, no.5 (2020) 1{13.
[14] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., NY, 2001.
[15] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, Berlin, 2014.

Files

History

  • Receive Date: 14 July 2022
  • Revise Date: 26 October 2022
  • Accept Date: 03 March 2023

Share

How to cite

Statistics