Binomial Transform of the Generalized Hexanacci Sequence
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, 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 Hexanacci sequence and as special cases, the binomial transform of the Hexanacci and Hexanacci-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: Pink gram breeding, Binomial transform, Cicer arietinum crosses, Hexanacci sequence, Hybrid vigour in Cicer arietinum, Hexanacci numbers, binomial transform of Hexanacci sequence, binomial transform of Hexanacci-Lucas sequence