Let n be a natural number, then s is the number of ways to write n as the sum of at least one natural number. What is the number s called?
If the addends are not necessarily distinct and order is not considered, then we have Partition Function P. And here is the Wikipedia article.
This is the number of compositions of n.
Thanks for replying. I made the conjecture that the number of compositions is $\displaystyle 2^{n-1}$, but I haven't been able to prove it. I don't understand the proof on wikipedia much either... I shamefully don't know anything about combinatorical proof..