The general form of the example given is 1 + 3 + 5 + ... + (2n - 1) + ... + 5 + 3 + 1 = (n - 1)2 + n2

, for n = 1001: 1 + 3 + 5 + ... + 1999 + 2001 + 1999 + ... + 5 + 3 + 1 = 10002 + 10012 = 2002001