Dude died at a power of 2 which is also the number of squares on a chess board. Poetic.
1, 8x8 square 4, 7x7 squares 9, 6x6 squares 16, 5x5 squares 25, 4x4 squares 36, 3x3 squares 49, 2x2 squares 64, 1x1 squares
The number of squares on a chessboard is infinite, if you don't limit yourself to edges already drawn for you.
By thy way:
sum(i=1..n) i*i = n/6 + n^2/2 + n^3/3From that: sum bla= n(n+1)(2n+1)/6, then you go distribute
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.