Školjka

%V0 Let $T$ denote the set of all ordered triples $\left(p,q,r\right)$ of nonnegative integers. Find all functions $f: T \rightarrow \mathbb{R}$ satisfying $$f(p,q,r) = \begin{cases} 0 &\text{if}\; pqr = 0,\\ 1+\frac{1}{6}(f(p+1,q-1,r)+f(p-1,q+1,r) &\\ +f(p-1,q,r+1)+f(p+1,q,r-1) &\\ +f(p,q+1,r-1)+f(p,q-1,r+1)) &\text{otherwise}\end{cases}$$ for all nonnegative integers $p$, $q$, $r$.