Another sphere where we meet fractions of bit is a data compression. Here you can often see expressions like "0.78 output bits per one input byte" meaning compression ratio.
Easy-to-make algorithms will go into deep-deep recursion, so it is not easy to make really fast one.
For example, shown code in Pascal will fall even on low parameters like p(200,20,20).
After some thinking I wrote algorithm which gives result in suitable time for p(125000,500,500).
It uses...
After long and careful search on the web and in literature,
I could not find the solution of the following problem.
I need calculate p(N,K,L) - the number of partitions of N into
no more than K parts not exceeding L.
Example: N = 7, K = 4, L = 5
1) 2+5
2) 3+4
3) 1+1+5
4) 1+2+4
5) 1+3+3
6)...