Product sum

Given a set of variables x_1, x_2, \ldots, x_N. Each variable x_i can take on only the values $-1$, $0$, or $+1$. For a given integer $S$, determine the number of ways to assign values to the variables x_i such that the sum of all possible products x_i \cdot x_j is equal to $S$, where i < j and i, j = 1, 2, \ldots, N. Two ways are considered different if they contain a different number of x_i = 0.