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

Abstract

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