On a study of (s, t)-generalized pell sequence and its matrix sequence

Abstract

First of all in this article, we consider (s, t)-type sequences such as (s, t)-Pell sequence hPn (s, t)i, (s, t)-Pell-Lucas sequence hQn (s, t)i and (s, t)-Modified Pell sequence hRn (s, t)i. Also we consider (s, t)- type matrix sequences such as(s, t)-Pell matrix sequence hUn (s, t)i, (s, t)- Pell-Lucas matrix sequence hVn (s, t)i and (s, t)-Modified Pell matrix sequence hWn (s, t)i. Then we introduce (s, t)-generalized Pell sequence hTn (s, t)i and its matrix sequence named (s, t)-generalized Pell matrix sequence hXn (s, t)i. But the main aim here to present many new results for (s, t)-generalized Pell sequence and (s, t)-generalized Pell matrix sequence and study the relations for (s, t)-generalized Pell sequence and (s, t)-generalized Pell matrix sequence with other (s, t)-type sequences and (s, t)-type matrix sequences. In addition to this we also define matrix sequences to (s, t)-type matrix sequences.