We obtain it by summing the pascal triangle (11, 121, 1331,...) with this... 2 4 2 6 4 2 8 10 4 2 10 18 14 4 2 12 28 32 18 4 Triangle above is obtained by summing the identical triangle like this... 1 2 1 3 2 1 4 5 2 1 5 9 7 2 1 6 14 16 9 4 While this is obtained by summing pascal triangle (11,121,1331,...) with this 0 1 0 1 1 0 1 2 1 0 1 3 3 1 0 1 4 6 4 1 And now it's easy to find that the desired formula is $ \frac{(n)(n-1)(n-2)(n-3}{8}+\frac{(n-1)(n-2)(n-3)}{3}$.

$ 3C_{n-1}^4+5C_{n-1}^{3}$