The Frequency of Summands of a Particular Size in Palindromic Compositions

Abstract

A composition of a positive integer $n$ consists of an ordered sequence of positive integers whose sum is $n$. A palindromic composition is one for which the sequence is the same from left to right as from right to left. This paper shows various ways of generating all palindromic compositions, counts the number of times each integer appears as a summand among all the palindromic compositions of $n$, and describes several patterns among the numbers generated in the process of enumeration.