Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$

Authors : Nacima Rosa AIT-AMRANE, Hacène BELBACHİR

Pages : 680-699

Doi:10.15672/hujms.825908

View : 18 | Download : 4

Publication Date : 2022-06-01

Article Type : Research Paper

Abstract :In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, bi-periodic $r$-Lucas sequence of type $s$ with $1 \leq s \leq r$, which extend the classical Fibonacci and Lucas sequences. Afterwards, we establish the link between the bi-periodic $r$-Fibonacci sequence and its companion sequences. Furthermore, we give their properties as linear recurrence relations, generating functions, explicit formulas and Binet forms.
Keywords : bi periodic r Fibonacci sequence, bi periodic r Lucas sequence, companion sequence, recurrence relation, generating function, explicit formula, Binet form