Number of ways a natural number can be written as sum of smaller natural number It is easy to realize that given a natural number N the number of doublets that sum N are
$\frac{N+(-1)(N \pmod 2)}{2}$ , so I thought I could reach some recursive formula in the sense that found the number of doublets I could find the number of triplets and so on ...,  example:
N=3 the only doublet is 2+1=3 -not said yet but 2+1, and 1+2 count as one- then I could count the number of way the number 2 can be expressed as the indicated sum and got the total number of ways 3 can be written as a sum. But this seems not so efficient, so I was wondering if there is other way to attack the problem and if there is some reference to this problem such as if it is well known its used, once I read that this have a chaotic behavior, and also read It was used in probability but don't remember where I got that information. So if you know something I would be grateful to be notice, thanks in advance.

You are asking about integer partitions. This is a well studied topic and you can look at http://en.wikipedia.org/wiki/Integer_partitions for details.
