MathNet 2023-part-06 — 191 problems (EN–VI) Question 2

Prove that for every $n \ge 1$, then $v_3(u_n) = v_3(n)$, where $(u_n)$ is the sequence with $u_0 = 0$, $u_1 = 1$ and
$$
u_{n+2} = 2u_{n+1} + 2u_n, \forall n \ge 0.$$