The matrix sequence in terms of bi-periodic Fibonacci numbers

Authors : Arzu COSKUN, Necati TASKARA

Pages : 1939-1949

Doi:10.31801/cfsuasmas.571975

View : 12 | Download : 9

Publication Date : 2019-08-01

Article Type : Research Paper

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