- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 3
- Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$
Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$
Authors : Nacima Rosa Ait-amrane, Hacène Belbachir
Pages : 680-699
Doi:10.15672/hujms.825908
View : 11 | Download : 4
Publication Date : 2022-06-01
Article Type : Research
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