PL-OM 2009 Problem 6

Let $n$ be a natural number equal or greater than 3 . A sequence of non-negative numbers $(c_0,c_1,\ldots,c_n)$ satisfies the condition: $c_{p}c_{s}+c_{r}c_{t}= c_{p+r}c_{r+s}$ for all non-negative $p,q,r,s$ such that $p+q+r+s=n$ . Determine all possible values of $c_2$ when $c_1=1$ .