On the Generalized $k$-Pell $(p,i)$-Numbers

Abstract

The current article focuses on the generalized $k$-Pell $(p,i)$-numbers for $k=1,2,\dots$ and $0\le i\le p$. It introduces the generalized $k$-Pell $(p,i)$-numbers and their generating matrices and generating functions. Some interesting identities are established.