If $f(x)$ is a real valued function satisfying $f(x+1)+f(x-1)=2f(x)$ $\forall x\in R$ and $f(0)=0$, then for any $n\in N,\:f(n)$ = ?

Question

$\begin{array}{1 1} nf(1) \\ [f(1)]^n \\ 0 \\ none\;of\;these \end{array}$