Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences

Abstract

In this paper we consider a generalized bi-periodic Fibonacci {f(n)}and a generalized bi-periodic Lucas sequence{q(n)}which are respectively defined by f(0)=0, f(1)=1, f(n)=af(n-1)+cf(n-2)(n is even) or f(n)=b(fn-1+)cf(n-2) (n is odd), and q(0)=2d,q(1)=ad,q(n)=bq(n-1)+cqn(-2)(n is even) or q(n)=af(n-1)+cq(n-2) (n is odd). We obtain various relations between these two sequences.