Count the rolls of n dice that allow a sum of s to be formed; see http://math.stackexchange.com/questions/1737961.

Question1737961.java

public class Question1737961 {
	final static int nsides = 6;
	
	public static void main (String [] args) {
		for (int n = 3;n <= 5;n++) {
			for (int s = 2;s <= nsides + 1;s++)
				System.out.println (n + ", " + s + " : " + recurse (new int [n],0,s));
		}
	}
	
	static int recurse (int [] a,int i,int s) {
		if (i == a.length) {
			for (int j = 1;j < a.length;j++)
				for (int k = 0;k < j;k++)
					if (a [j] + a [k] == s)
						return 1;
			return 0;
		}
		int sum = 0;
		for (a [i] = 1;a [i] <= nsides;a [i]++)
			sum += recurse (a,i + 1,s);
		return sum;
	}
}