On Binomial Transform of the Generalized Fifth Order Pell Sequence
Yüksel Soykan *
Department of Mathematics, Faculty of Art and Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we define the binomial transform of the generalized fifth order Pell sequence and as special cases, the binomial transform of the fifth order Pell and fifth order Pell-Lucas sequences will be introduced. We investigate their properties in details. We present Binet’s formulas, generating functions, Simson formulas, recurrence properties, and the summation formulas for these binomial transforms. Moreover, we give some identities and matrices related with these binomial transforms.
Keywords: Binomial transform, fifth order Pell Sequence, fifth order Pell numbers, binomial transform of fifth order Pell Sequence, binomial transform of fifth order Pell-Lucas sequence