A Motzkin Variation on The Tennis Ball Problem

Naiomi T. Cameron 1, Lynnell S. Matthews2
1Lewis & CLARK COLLEGE
2GETTYSBURG COLLEGE

Abstract

We consider a variation on the Tennis Ball Problem studied by Mallows-Shapiro and Merlini, \(et \;al\). The solution to the original problem is the well known Catalan numbers, while the variations discussed in this paper yield the Motzkin numbers and other related sequences. For this variation, we present a generating function for the sum of the labels on the balls.