Linear recurrence sequence in F2

Question

Currently, I'm solving this exercise:

Let $s= (s_0,s_1,s_2,...)$ be a linear recurrence sequence in $F_2$ with recurrent relation $s_{n+3}+s_{n+1}+s_n= 0$, for $n\in \mathbb N$.

Now my (simple) question: What's the period of the relation?

Thanks for any help! :)

Answer 1

(EDITED) Hint: if $s_k = s_0$, $s_{k+1} = s_1$, and $s_{k+2} = s_2$, the sequence will be periodic with period $k$.