0, 1, 4, 9... what is this classical sequence?

I don't know if this is what you're looking for, but that's a sequence
of squares. You have the squares of 0, 1, 2, and 3. Next would come
16, 25, 36, and so on (the squares of 4, 5, 6, etc.)

Pink is right.  The word you are looking for is: sqaures

But only if you spell it correctly, unlike myself: squares