nsumk

Little more than syntactic sugar for nchoosek, this small but surprisingly controversial function returns the number of (ordered) n-tuples of non-negative integers adding up to k, and if supplied a second argument, a listing of them. As an alternative to downloading, just cut and paste the following:

m = nchoosek(k+n-1,n-1);
dividers = [zeros(m,1),nchoosek((1:(k+n-1))',n-1),ones(m,1)*(k+n)];
x = diff(dividers,1,2)-1;

It has been noted with some passion that this it is possible to achieve the same result using partitions.m, a more general function posted on Matlab Central. Indeed nsumk(n,k) returns the same result as sortrows(partitions(k, ones(1,n))). For small problems the latter is probably no more than 10x slower than using nchoosek. For large problems the performance of nsumk is substantially better (but only because we desire a special ordering).

These observations may be more relevant to others than this author, and no effort has been made to optimize nsumk (or for that matter nchoosek). See vchoosek.m for a faster .mex implementation of nchoosek.