__,__,__,48,100,180, 294,448,648,__,__,__,.......Find the three numbers before and after given numbers in the series.

(In reply to re: Solution by differences by Hugo)

The numbers that pop out of the differencing can be used with binominal coefficients to get the formula straight away.  The formula would be 4 x (n choose 1) + 10 x (n choose 2) + 6 x (n choose 3) where the third term is 48.  This reduces to n x (n+1) x (n+1).  There is also a component, 0 x (n choose 0), that can be dropped, due to the "zeroeth" term of the series being zero.

Posted by bernie on 2005-04-28 22:30:58