The sum of the first n odd numbers is a square number, sum_(k = 1)^n(2k - 1) = n^2. A sort of converse also exists, namely the difference of the nth and (n - 1)st square numbers is the nth odd number, which follows from n^2 - (n - 1)^2 = 2n - 1.

gnomonic number | Nicomachus's theorem | odd number | sum