Some properties of generalized $k$-Pell sequences

TL;DR

This paper develops identities for generalized $k$-Pell sequences and explores applications of tridiagonal matrices, enhancing understanding of their properties and potential uses.

Contribution

It introduces new identities for generalized $k$-Pell sequences and investigates their applications via tridiagonal generating matrices.

Findings

Derived identities including Binet, Catalan, Cassini, and d'Ocagne formulas.

Established applications of tridiagonal matrices to these sequences.

Enhanced understanding of the properties of generalized $k$-Pell sequences.

Abstract

The purpose of this paper is twofold; (1) to develop several identities for the Generalized $k$-Pell sequence (including those of Binet, Catalan, Cassini, and d'Ocagne), and (2) to study applications of tridiagonal generating matrices for the $k$-Pell and Generalized $k$-Pell sequences.