Iterated binomial transform of the k-Lucas sequence

TL;DR

This paper investigates the iterated binomial transform of the k-Lucas sequence, deriving formulas and properties, and comparing it with classical Lucas sequences to deepen understanding of its mathematical structure.

Contribution

It introduces the application of multiple binomial transforms to the k-Lucas sequence and derives related formulas and properties, expanding the theoretical framework.

Findings

Derived Binet formula, summation, and generating function for the iterated binomial transform

Established properties of the transform in relation to classical Lucas sequence

Analyzed recurrence relations of the transformed sequence

Abstract

In this study, we apply "r" times the binomial transform to k-Lucas sequence. Also, the Binet formula, summation, generating function of this transform are found using recurrence relation. Finally, we give the properties of iterated binomial transform with classical Lucas sequence.