Number of partitions of an integer into four parts

Asked Jun 06 '18 at 12:16

Active Jun 06 '18 at 12:24

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I'm interested in the following question: find the number of partitions of an integer (for example, 1000) into 4 parts not exceeding given bound (for example, 511). How to approach this? If there was no restrictions for parts, the answer would be $C_{1003}^3$, but I don't know how to take into account those restrictions. Any suggestions?

Edit: parts don't have to be distinct.

edited Jun 06 '18 at 12:24

asked Jun 06 '18 at 12:16

CuriousGuest

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Thanks, but in that question they require parts to be distinct, I don't have such a restriction. – CuriousGuest Jun 06 '18 at 12:23
This is also covered here at MSE; you can use this question for at most $3$ and $4$ parts, and then substract. – Dietrich Burde Jun 06 '18 at 12:26
It's still not clear to me how to use recurrence relation for $p(l,k,n)$ to calculate $p(511,4,1000)$. Can anyone help? – CuriousGuest Jun 06 '18 at 12:35
Also, I think for this particular case must be simpler approach. – CuriousGuest Jun 06 '18 at 12:47

Number of partitions of an integer into four parts

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