A determinant of generalized Fibonacci numbers

TL;DR

This paper evaluates a determinant involving generalized Fibonacci numbers, unifying various existing determinant identities and extending Cassini's identity to a broader class of Fibonacci-like sequences.

Contribution

It introduces a generalized determinant formula for Fibonacci numbers, extending classical identities and unifying previous results in the literature.

Findings

Derived a general determinant formula for generalized Fibonacci numbers

Unified multiple existing determinant identities

Extended Cassini's identity to generalized Fibonacci sequences

Abstract

We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.