I found the equation , then I found $S_3$ :
$$S_3-S_1-3=0$$
And I found $S_3$
Also I gave it a try using the Generalized form:
$$S_n+S_{n-2}+S_{n-3}=0$$
Let $n=0$
$$S_1+S_{-1}+S_{-2}=0$$
Now I can't find $S_{-1}$ in order to find $S_{-2}$
How to find $S_{-2}$ ? Any help is much appreciated.