Algorithm 448: number of multiply-restricted partitions

Given a positiver integer m and an ordered k -tuple c = ( c 1 , ··· , c k ) of not necessarily distinct positive integers, then any ordered k -tuple s = ( s 1 , ··· , s k ) of nonnegative integers such that m = ∑ k i -1 s i c i is said to be a partition of m restricted to c . Let P c ( 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 P c ( m ) for m = 1 to n . Many combinatorial enumeration problems may be expressed in terms of the numbers P c ( m ). We mention two below.