Question 149
Let say a 52-digit number $\overline{a_1a_2\ldots a_{52}}$ is "zig-zag" if
$$
a_1 \le a_2 \ge a_3 \le a_4 \ge \dots \le a_{50} \ge a_{51} \le a_{52}
$$
holds. Find the number of all zig-zag numbers composed of the digits $1$, $2$ and $3$.
$$
a_1 \le a_2 \ge a_3 \le a_4 \ge \dots \le a_{50} \ge a_{51} \le a_{52}
$$
holds. Find the number of all zig-zag numbers composed of the digits $1$, $2$ and $3$.