How many permutations $s$ does the set $\{1,2,..., 15\}$ have with the following properties: for every $1 \le k \le 13$ we have $s(k) < s(k+2)$ and for every $1 \le k \le 12$ we have $s(k) < s(k+3)$?
Problem
Source: 2019 Dürer Math Competition Finals Day2 E+5 https://artofproblemsolving.com/community/c1621835_2019_
Tags: permutation, combinatorics