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?)
