+864 If $n$ is a positive integer, a $3$-partition of $n$ is a list of powers of $3$, arranged in order from greatest to least, whose sum is $n.$ For example, there are three $3$-partitions of $6,$ namely $3-3, 3-1-1-1$ and $1-1-1-1-1-1.$ How many different $3$-partitions of $8$ are there?
