KöMaL 2021 B5206

An $n$-digit number $\overline{a_1a_2a_3\ldots a_n}$ is called hill type if there exists an integer $1 \le k \le n$ for which the sequence $a_1,a_2,\ldots,a_k$ is strictly increasing and the sequence $a_k,a_{k+1},\ldots,a_n$ is strictly decreasing. (For example, the numbers 1, 121, 1231 are of hill type, whereas 1442 or 12313 are not.) How many hill type numbers are there?