Generating functions of lattice paths

Abstract

We recall the main types of \emph{lattice paths}, which are sequences in the lattice of integer coordinates points in the plane. We start with the fundamental \emph{central lattice paths} and \emph{Dyck paths} and proceed in elementary terms through recently introduced lattice paths.

For every type, we consider the respective \emph{generating function}. In fact, through our approach (via \emph{Riordan arrays}), various entries of the On-Line Encyclopedia of Integer Sequences are unified, clarified, and simplified.