Special Matrices Associated with Generalized Fibonacci Numbers

TL;DR

This paper develops a method to construct special 3x3 matrices whose powers relate to Horadam and generalized Fibonacci numbers, extending previous work on matrices associated with Fibonacci and Lucas numbers.

Contribution

The paper introduces a new method for deriving 3x3 matrices linked to generalized Fibonacci sequences, expanding the class of matrices associated with these numbers.

Findings

Derived new 3x3 matrices related to Horadam and generalized Fibonacci numbers

Established relationships between matrix powers and these sequences

Extended previous methods for Fibonacci and Lucas matrices

Abstract

In \cite{Ka}, the authors obtained a method for deriving special matrices, whose powers are related to Fibonacci and Lucas numbers. In the study, it has been developed a method for deriving special matrices of $3\times 3$ dimensions, whose powers are related to Horadam and generalized Fibonacci numbers, and some special matrices have been found via the method developed.