Question 24
Define the sequence $a_{0}, a_{1}, a_{2}, \ldots$ by $a_{n}=2^{n}+2^{\lfloor n / 2\rfloor}$. Prove that there are infinitely many terms of the sequence which can be expressed as a sum of (two or more) distinct terms of the sequence, as well as infinitely many of those which cannot be expressed in such a way.