How many ways can you make the sum of a number? From wikipedia: https://en.wikipedia.org/wiki/Partition_(number_theory)#
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 Examples Basic sum(1) // 1 sum(2) // 2 -> 1+1 , 2 sum(3) // 3 -> 1+1+1, 1+2, 3 sum(4) // 5 -> 1+1+1+1, 1+1+2, 1+3, 2+2, 4 sum(5) // 7 -> 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 1+4, 5, 2+3
sum(10) // 42 Explosive sum(50) // 204226 sum(80) // 15796476 sum(100) // 190569292