#include "stdio.h"
#include "math.h"

#define PI 3.14159265358979323846 

/*
The number of ways to tile an MxN rectangle with 1x2 dominos is 2^(M*N/2) times the product of

{ cos^2(m*pi/(M+1)) + cos^2(n*pi/(N+1)) } ^ (1/4)

over all m,n in the range 0<m<M+1, 0<n<N+1.
*/

double nr_DT(int N, int M)
{
	double f = 1;
	
	for (int n = 1; n < N+1; n++)
	{
		for (int m = 1; m < M+1; m++)
		{
			double v1 = cos(m*PI/(M+1));
			double v2 = cos(n*PI/(N+1));
			f *= sqrt(sqrt(4*(v1*v1 + v2*v2)));
		}
	}
	
	return f;
}

int main(int argc, char* argv[])
{
	for (int N = 2; N < 20; N++)
		for (int M = N; M < 20; M++)
			if (N*M % 2 == 0)
			{
				printf("%d x %d: %lf\n", N, M, nr_DT(N,M));
			}
}