Identities for the k-generalized Fibonacci sequence with negative indices and its zero-multiplicity

TL;DR

This paper derives identities for the k-generalized Fibonacci sequence at negative indices and uses these to determine the exact number of zeros in the sequence.

Contribution

It introduces new identities for negative indices in the k-generalized Fibonacci sequence and applies them to find its zero-multiplicity.

Findings

Derived identities for negative indices in the sequence

Established an exact formula for zero-multiplicity

Enhanced understanding of sequence behavior at negative indices

Abstract

In this paper, we prove identities for members of the k-generalized Fibonacci sequence with negative indices and we apply these identities to deduce an exact formula for its zero-multiplicity.