There is a recurrence relation, but no compact formula has been found yet.
Partition (number theory) - Wikipedia, the free encyclopedia
Hi, could someone help me with this problem - suppose I have s identical balls that I want to put in n identical boxes - in how many different way can I do this?
For example: s=3, n=3:
|ooo|||
|oo|o||
|o|o|o|
So the answer is 3.
s=6, n=2:
|oooooo||
|ooooo|o|
|oooo|oo|
|ooo|ooo|
So the answer is 4.
It's easy to do it ad hoc, but the general principle escapes me.
Thanks!
There is a recurrence relation, but no compact formula has been found yet.
Partition (number theory) - Wikipedia, the free encyclopedia
I'm not sure if the Wikipedia page has the recurrence the OP is after. We can sum the function P(n, k) given here
Partition Function P -- from Wolfram MathWorld
after equation (54) from 1 to k. Also, it's mentioned here, lower left cell
http://www.johndcook.com/TwelvefoldWay.pdf