Recurrence Relations and Linear-Feedback Shift Registers I have an exercise for a cryptography/number theory course that I'm trying to work on. 
In the exercise, I have a Linear Feedback Shift Register which is working in mod 3 with digits  {0,1,2}.  
The LFSR is using a recurrence relation of degree 2, which looks like the following
$$Z_{i+2}=C_0Z_i+C_1Z_{i+1}$$ 
I also have a part of the keystream $S=...11022...$
I am looking to find $C_0$ & $C_1$ along with the three keystream numbers that follow and precede $S$.
Unfortunately I have no examples to work off so I'm confused on how i'd start even with finding $C_0$ & $C_1$?
The only example I have from class is with the initial part of the keystream.

Via method described in comments presuming each digit of $Z$ is a digit of $S$ $\mod 3$ I get the following;
$$C_0=2$$
$$C_1=1$$
$$S=22011022011$$
