Question 172
Given a positive integer $n$. Denote by $T$ the set of the first $2n$ positive integers. Find the number of subsets $S$ of $T$ with the property: in $S$ there do not exist numbers $a, b$ with $|a-b| \in \{1; n\}$.
(Note: The empty set is considered as satisfying the above property).
(Note: The empty set is considered as satisfying the above property).