Algorithm 448: number of multiply-restricted partitions

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Abstract
Given a positiver integer m and an ordered k-tuple c = (c1, ··· , ck) of not necessarily distinct positive integers, then any ordered k-tuple s = (s1, ··· , sk) of nonnegative integers such that m = ∑ki-1 sici is said to be a partition of m restricted to c. Let Pc(m) denote the number of distinct partitions of m restricted to c. The subroutine COUNT, when given a k-tuple c and an integer n, computes an array of the values of Pc(m) for m = 1 to n. Many combinatorial enumeration problems may be expressed in terms of the numbers Pc(m). We mention two below.