Number of combinations of integers \leq n which sum to n

[mapkan]

Hi all,
I'm new to the forum, this is my problem:

given a positive integer n, i want to find how many combinations of integers smaller than n but larger than 0 sum to n. E.g.

n=3:
{3},{2,1},{1,1,1}

n=4:
{4},{3,1},{2,2},{2,1,1},{1,1,1}

it might just be that I'm tired, but I've been thinking about this for a while.

Thank you very much!

 

[pmsrw3]

http://en.wikipedia.org/wiki/Partition_%28number_theory%29" .

 

[mapkan]

http://en.wikipedia.org/wiki/Partition_%28number_theory%29" .

Thank you very much!
Perfect!