The matrix sequence in terms of bi-periodic Fibonacci numbers

Year 2019, Volume: 68 Issue: 2, 1939 - 1949, 01.08.2019

Arzu Coskun , Necati Taskara

https://doi.org/10.31801/cfsuasmas.571975

Cited By: 2

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, we say that some behaviours of bi-periodic Fibonacci numbers can be obtained via the properties of this new matrix sequence. Finally, we express that well-known matrix sequences such as Fibonacci, Pell, k-Fibonacci matrix sequences are special cases of this generalized matrix sequence.

Keywords

Bi-periodic Fibonacci matrix sequence, bi-periodic Fibonacci numbers, Binet formula, generating function

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