Count the number of tilings of an n by n square with n rectangles of integer sides and area n

Question130758.java

// Count the number of tilings of an n by n square with n rectangles of integer sides and area n
// See http://math.stackexchange.com/questions/130758

public class Question130758 {
    final static int maxn = 100;

    static int n;
    static int [] divisors = new int [maxn];
    static int ndivisors;
    static boolean [] [] grid;
    static int count;
    
    public static void main (String [] args) {

	for (n = 1;n <= maxn;n++) {
	    ndivisors = 0;
	    for (int divisor = 1;divisor <= n;divisor++)
		if (n % divisor == 0)
		    divisors [ndivisors++] = divisor;

	    grid = new boolean [n] [n];
	    count = 0;
	    recurse (0,0,0);
	    System.out.println (n + " : " + count);
	}
    }

    static void recurse (int x,int y,int depth) {
	if (depth == n) {
	    count++;
	    return;
	}

	while (grid [x] [y])
	    if (++x == n) {
		x = 0;
		y++;
	    }

	outer:
	for (int k = 0;k < ndivisors;k++) {
	    int w = divisors [k];
	    int h = n / w;
	    if (x + w > n || y + h > n)
		continue;
	    for (int i = 0;i < w;i++)
		for (int j = 0;j < h;j++)
		    if (grid [x + i] [y + j])
			continue outer;
	    for (int i = 0;i < w;i++)
		for (int j = 0;j < h;j++)
		    grid [x + i] [y + j] = true;
	    recurse (x,y,depth + 1);
	    for (int i = 0;i < w;i++)
		for (int j = 0;j < h;j++)
		    grid [x + i] [y + j] = false;
	}
    }
}