Generating matrix of the bi-periodic Lucas numbers

TL;DR

This paper introduces a generating matrix for bi-periodic Lucas numbers and explores its properties, providing new insights into their structure and relationships with bi-periodic Fibonacci numbers.

Contribution

The paper presents the first Q_{l}-Generating matrix for bi-periodic Lucas numbers and derives properties connecting them with bi-periodic Fibonacci numbers.

Findings

Introduction of Q_{l}-Generating matrix for bi-periodic Lucas numbers

Derivation of properties linking bi-periodic Lucas and Fibonacci numbers

Matrix representation enhances understanding of bi-periodic sequences

Abstract

In this paper, firstly, we introduce the Q_{l}-Generating matrix for the bi-periodic Lucas numbers. Then, by taking into account this matrix representation, we obtain some properties for the bi-periodic Fibonacci and Lucas numbers.