Determinants of Rising Powers of Second Order Linear Recurrence Entries by Means of the Desnanot-Jacobi Identity

TL;DR

This paper uses the Desnanot-Jacobi identity to provide an alternative proof for determinants involving rising powers of Fibonacci numbers and generalizes these results to second order linear recurrence entries.

Contribution

It introduces a novel application of the Desnanot-Jacobi identity to determinants of rising powers of recurrence sequences, extending previous Fibonacci-based results.

Findings

Alternative proof for Fibonacci power determinants

Generalization to second order linear recurrences

Broader applicability of the Desnanot-Jacobi identity

Abstract

We apply the Desnanot-Jacobi identity to give an alternative proof of the determinants whose entries are rising powers of the Fibonacci numbers given by Prodinger. We then generalize the determinants to include entries that are rising powers of the terms in a second order linear recurrence.