Certain Binomial Sums with recursive coefficients

TL;DR

This paper derives new identities involving binomial sums with coefficients following third-order linear recursions, generalizing previous identities related to Fibonacci-like sequences.

Contribution

It introduces general forms of binomial sum identities with recursive coefficients, extending earlier results involving Fibonacci-type sequences.

Findings

New identities for binomial sums with recursive coefficients

Generalized forms of identities involving Fibonacci-like sequences

Connections between binomial sums and third-order linear recursions

Abstract

In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving binomial coefficients and Fibonacci type sequences.