[2.4] Exercise 7
Let \(\lfloor x \rfloor\) denote the largest integer smaller than or equal to \(x\). Use Theorem 1 to prove that \(\lfloor n/3 \rfloor + 1\) is the number of partitions of \(n\) into distinct parts where each part is either a power of two or three times a power of two. [TODO]
Example 1
$$
\begin{align}
6 &= 1 + 1 + 1 + 1 + 1 + 1 \\
6 &= 2 + 2 + 1 + 1 \\
6 &= 2 + 1 + 1 + 1 + 1 \\
6 &= 4 + 1 + 1 \\
6 &= 4 + 2 \\
6 &= 3 + 1 + 1 + 1 \\
6 &= 3 + 2 + 1 \\
6 &= 3 + 3 \\
6 &= 2 + 2 + 2 \\
6 &= 5 + 1 \\
6 &= 6
\end{align}
$$