In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. If order matters, the sum becomes a composition. For example, 4 can be partitioned in five distinct ways:
4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1
Basic
exp_sum(1) // 1
exp_sum(2) // 2 -> 1+1 , 2
exp_sum(3) // 3 -> 1+1+1, 1+2, 3
exp_sum(4) // 5 -> 1+1+1+1, 1+1+2, 1+3, 2+2, 4
exp_sum(5) // 7 -> 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 1+4, 5, 2+3
exp_sum(10) // 42
Explosive
exp_sum(50) // 204226
exp_sum(80) // 15796476
exp_sum(100) // 190569292