F[i][j]=F[i-j-1][j+1]+F[i][j+1];
cout << F[N-1][0]-1<< endl;;

F[i][j] corresponds to staircase using i bricks with height of 1st step>=j.
height of 1st step will either be j in  which case, it will give f[i-j-1][j+1]
or it will be greater than j, in which case it is just f[i][j+1].