Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials

TL;DR

This paper simplifies the understanding of recurrences in binomial sum sequences using generalized Fibonacci and Lucas polynomials, providing clearer insights into their mathematical structure.

Contribution

It offers a streamlined presentation of recurrence relations for binomial sum sequences expressed through generalized Fibonacci and Lucas polynomials.

Findings

Recurrences are expressed in simplified forms.

Connections between binomial sums and Fibonacci/Lucas polynomials are clarified.

Mathematical structure of these sequences is better understood.

Abstract

We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.