Let $S\_1$ denote the sequence $(1,1)$.

For $n\ge 1$, we build a sequence $S\_{n+1}$ by copying sequence $S\_n$, inserting blanks between consecutive terms, and filling each blank with the sum of the two terms it's between. Thus we have
\begin{align\*}
S\_2 &= (1,\underline{2},1),\\
S\_3 &= (1,\underline{3},2,\underline{3},1),\\
S\_4 &= (1,\underline{4},3,\underline{5},2,\underline{5},3,\underline{4},1),
\end{align\*}
and so on.

* What is the sum of all entries in $S\_7$?
* What is the largest entry in sequence $S\_{11}$?
* What fraction of the terms of $S\_{64}$ are odd?