Elif TAN

A Q-ANALOG OF THE BI-PERIODIC LUCAS SEQUENCE

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

Keywords:

bi-periodic Fibonacci and Lucas sequences,

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E-mail address : etan@ankara.edu.tr Current address : Department of Mathematics, Faculty of Sciences, Ankara University, 06100
Tandogan Ankara, Turkey ORCID Address: http://orcid.org/0000-0002-8381-8750