Question 18
A non-empty set $A \subseteq \{1, 2, 3, \dots, n\}$ is called a *good set* of degree $n$ if $|A| \le \min_{x \in A} x$. Denote by $a_n$ the number of good sets of degree $n$. Prove that $a_{n+2} = a_{n+1} + a_n + 1$ for any positive integer $n$. (posed by Li Weigu)