English

The Matrix Sequence in terms of bi-periodic Fibonacci numbers

Number Theory 2016-04-05 v2

Abstract

In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we say that some behaviours of bi-periodic Fibonacci numbers also can be obtained by considering properties of this new matrix sequence. Finally, we express that well-known matrix sequences, such as Fibonacci, Pell, kk-Fibonacci matrix sequences are special cases of this generalized matrix sequence.

Keywords

Cite

@article{arxiv.1603.07487,
  title  = {The Matrix Sequence in terms of bi-periodic Fibonacci numbers},
  author = {Arzu Coskun and Necati Taskara},
  journal= {arXiv preprint arXiv:1603.07487},
  year   = {2016}
}