For a proof by induction exercise, I'm given a sequence defined recursively as $s_0 = 0, s_1 = 1, s_2 = 0; s_n := s_{n-3} + s_{n-2} - s_{n-1}$ for $n \geq 3$ and I am asked to make a guess for the general form of $s_n$. However, I'm struggling to come up with the general form, as from what I've calculated, the sequence simply goes back and forth between $0$ and $1$. I've tried a few guesses with floor functions and even a sine function, but they all don't seem to work or is not what the exercise expects me to prove.
So could I ask for some guidance in finding the general form? If I have the general form I'm pretty confident that I can use induction to prove it so I don't really want the proof, only the general form. Thanks!