I want to solve this problem:
The number 6 can be written as a palindromic sum in exactly eight different ways:
(1,1,1,1,1,1),(1,1,2,1,1),(1,2,2,1),(1,4,1),(2,1,1,2),(2,2,2),(3,3),(6) We shall define a twopal to be a palindromic tuple having at least one element with a value of 2. It >should also be noted that elements are not restricted to single digits. For example, (3,2,13,6,13,2,3) >is a valid twopal.
If we let t(n) be the number of twopals whose elements sum to n, then it can be seen that t(6)=4:
(1,1,2,1,1),(1,2,2,1),(2,1,1,2),(2,2,2) Similarly, t(20)=824.
In searching for the answer to the ultimate question of life, the universe, and everything, it can be >verified that t(42)=1999923, which happens to be the first value of t(n) that exceeds one million.
However, your challenge to the "ultimatest" question of life, the universe, and everything is to find the least value of n>42 such that t(n) is divisible by one million.
I quickly got the value of t(20) using the following method:
Count[(Flatten[Permutations /@ Evaluate[IntegerPartitions[20, All]], 1]) // DeleteDuplicates, u_ /; u == Reverse[u] && MemberQ[u, 2]]
However, when I use the above method to solve t(42), I am prompted that the memory is insufficient. How can I avoid memory overflow errors?