Let $N_0$ be the set of all non-negative integers and let $f : N_0 \times N_0 \to [0, +\infty)$ be a function such that $f(a, b) = f(b, a)$ and $$f(a, b) = f(a + 1, b) + f(a, b + 1),$$for all $a, b \in N_0$. Denote by $x_n = f(n, 0)$ for all $n \in N_0$. Prove that for all $n \in N_0$ the following inequality takes place $$2^n x_n \ge x_0.$$