I think it's so exciting that there's an online encyclopedia of integer sequences (linked to in the article: https://oeis.org/A000127)! Enter practically any sequence off the top of your head, and blam, there's a formula for it and background about it!
Numberphile has a bunch of fun videos starring Neil Sloane, the creator of the OEIS. He gets really excited about graphs
"Though the first five terms match the geometric progression 2n − 1, it diverges at n = 6, showing the risk of generalising from only a few observations."