This is a repost from r/math since I don't use reddit I can't post there. I think this is the most appropriate sister thread.
So a few years ago I noticed a pattern about differences of squared numbers. However, I failed to find anything about it. It just popped into my head again, and I am not conceited enough to think I invented 'new math' or whatever. So someone tell me this is a thing and I am just ignorant.
The concept goes as follows... the difference between the additive amounts of squared numbers is always two more than the last. At least when moving up integers. When moving down it decreases by 2. This is at the exclusion to 0^2.
Exemplified as follows:
1^2 | 2^2 | 3^2 | 4^2 | 5^2 |
1 4 9 16 25
+3 +5 +7 +9
+2 +2 +2
If what I put above is readable see how the difference of 3^2 (9) and 4^2 (16) is 7, then the difference of 4^2 (16) and 5^2 (25) is 9. Then notice how the difference of 7 and 9 is 2. And how it is always 2 between adjacent sets of squared results. This pattern goes on for as far as I checked.