Question 21
A set $S$ is called neighboring if it has the following two properties:
i) $S$ has exactly 4 elements,
ii) for every element $x \in S$ at least one of the numbers $x-1$ or $x+1$ belongs to $S$.
Find the number of all neighboring subsets of the set $\{1,2, \ldots, n\}$.
i) $S$ has exactly 4 elements,
ii) for every element $x \in S$ at least one of the numbers $x-1$ or $x+1$ belongs to $S$.
Find the number of all neighboring subsets of the set $\{1,2, \ldots, n\}$.