Weekly Problem 20 - 2013
The general form of the example given is $$1 + 3 + 5 + \dots + (2n
- 1) + \dots + 5 + 3 + 1 = (n - 1)^2 + n^2$$
Therefore, for $n = 1001$: $$1 + 3 + 5 + \dots + 1999 + 2001 + 1999
+ \dots + 5 + 3 + 1 = 1000^2 + 1001^2 = 2002001$$