I was playing around with the squares and saw an interesting pattern in their differences.
$0^2 = 0$
+ 1
$1^2 = 1$
+ 3
$2^2 = 4$
+ 5
$3^2 = 9$
+ 7
$4^2 = 16$
+ 9
$5^2 = 25$
+ 11
$6^2 = 36$
etc.
(Also, in a very related question, which major Math Research Journal should I contact to publish my groundbreaking find in?)