A Study on Binomial Transform of the Generalized Sixth Order Pell Sequence
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we dene the binomial transform of the generalized sixth order Pell sequence and as special cases, the binomial transform of the sixth order Pell and sixth 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 related with these binomial transforms.
Keywords: ABO blood and haptoglobin types, Binomial transform, Hp1 gene frequency, Hexanacci sequence, ABO incompatibility, sixth order Pell numbers, binomial transform of sixth order Pell sequence, binomial transform of sixth order Pell-Lucas sequence