sum of the costs of all antipalindromic sequences of length 2020
Source: 2020 New Zealand MO Round 2 p5 NZMO
September 22, 2021
combinatorics
Problem Statement
A sequence of s and s is called antipalindromic if writing it backwards, then turning all the s into s and vice versa, produces the original sequence. For example is antipalindromic. For any sequence of s and s we define the cost of the sequence to be the product of the positions of the s. For example, the string has cost . Find the sum of the costs of all antipalindromic sequences of length .