Suppose f: RxR -> R is has continuous partial derivatives and

4* f(x,y)=f(x+del,y+del)+f(x-del,y+del)+f(x-del,y-del) + f(x+del,y-del)

for all (x,y) in RxR and all del in R.

I dont believe that f is necessarly harmonic but I cannot construct a counter example. Is f harmonic?