[eru]

Nice. How did I get the result in the first place?

I know that this sum can be expressed as a cubic polynomial. So I just evaluated the sum at four data-points (n=0,1,2,3) and used those to determine the four coefficents by solving a linear equation system.

[jgrahamc]

Turns out that drawing a picture really helps: http://news.ycombinator.com/item?id=101532

[eru]

You can usually come up with a clever picture only after you understood the problem - not before.