A Q-ANALOG OF THE BI-PERIODIC LUCAS SEQUENCE

Abstract

In this paper, we introduce a q-analog of the bi-periodic Lucassequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we givea matrix representation for the q-bi-periodic Fibonacci sequence which allowus to obtain several properties of this sequence in a simple way. Moreover,by using the explicit formulas for the q-bi-periodic Fibonacci and Lucas sequences, we introduce q-analogs of the bi-periodic incomplete Fibonacci andLucas sequences and give a relation between them