Question 148
For a positive integer $n \gt 3$, a set $A$ of sequences of 0s and 1s of length $n+1$ is called *good* if any sequence of 0s and 1s of length $n$ can be obtained from a sequence from $A$ by deleting one term. Let $a_n$ be the minimum number of elements of a good set. Prove that: $\frac{2^n + 2n - 7}{n} \le a_n \le 2^{n-1}$.