CONVOLUTIONS OF THE GENERALIZED PELL AND PELL--LUCAS NUMBERS

Abstract

We consider the convolution  of the generalized  Pell numbers--$P_{n,m}^{(s)}$ and the convolution of the generalized Pell--Lucas numbers--$Q_{n,m}^{(s)}$.  For $s=0$, the sequence $P_{n,m}^{(0)}$ represents the  generalized Pell numbers $P_{n,m}$,  and the sequence $Q_{n,m}^{(0)}$ represents the  generalized Pell--Lucas numbers $Q_{n,m}$ (\cite 1, \cite 2).