Pell Walks and Riordan Matrices

Abstract

The purpose of this paper is twofold. As the first goal, we show that three different classes of random walks are counted by the Pell numbers. The calculations are done using a convenient technique that involves the Riordan group. This leads to the second goal, which is to demonstrate this convenient technique. We also construct bijections among Pell, certain Motzkin, and certain Schröder walks. As a consequence of using these Riordan group methods, we also find unexpected connections to a special class of Riordan matrices called Schröder matrices.