[math-fun] well posed problem?

of all subsets of the n-th roots of -1, n= 1 to 20, how many add to zero? ?? 0, 1, 1, 3, 1, 6, 1, 11, 4, 8, 1, 50, 1, 10, 9, 107, 1, 240, 1, 316 ?? where are the 'groupies' when you need them? W.