Weak Stream Cipher cryptanalysis
I'll expand my comments into a full answer. 

Start by examining that you know the value of $r^3$ - this is just $F(r)$. 

You know you can express $F(r+1)$ and $F(r+2)$ symbolically. You can do this for any term in the key sequence, but it will be useful to write down $F(r+3)$. Forget any constant terms in the computations because they can be added in at the end.

Do you notice anything about the coefficients of $r^2$ and $r$ in the expressions for $F(r+1)$ and $F(r+2)$? Do they look like the coefficients of any subsequent terms in the key sequence?