If one indexes the sequence from t, then the function for each term is trivially

Because this is the end of the easy sequences, you get something a bit more tricky - another solution:

Part of what mathematicians do is look for patterns. But be warned, just because it *looks* like it's doing something doesn't mean it's going to keep doing it forever! Showing that something does actually follow a pattern is some of what mathematicians spend their time on. But don't worry about that now, go look at some more sequences!

A bit too trivial for my liking, what about

resulting in 0, 1, 1, 1, 1, 1, 1, **2, 2, 2, 2...**

What about any of these?

with k >= 4

The sequence wasn´t supposed to necessarily change from 1 to 2 exactly after the ellipsis ("...").

another solution: with

f(n) = f(n-1) ! for n > 1 0, 1, 1, 1, 1, 1, 1, **1, 1, 1, 1...**