TopsOJ Summer 2025 - Individual Round - Problem 13

A string of digits d_1d_2 \ldots d_n that can start with 0 is denoted as *peaked* if d_1=d_n and there is some digit d_k other than d_1 and d_n, such that d_1<d_2<\ldots<d_k and d_k>d_{k+1}>\ldots>d_n. Compute the number of peaked strings with at least 3 digits.