Combinatorial Identities for the Narayana Numbers

Abstract

We interpret the Narayana numbers combinatorially by having them count the number of tilings of an n-strip using squares and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Narayana numbers. Additionally, these techniques are used to introduce the generalized Narayana numbers and the k-Narayana numbers and to prove corresponding identities.