Ways to partition a block of 9 into blocks of sizes 1, 2, and 3 How many ways are there to partition a block of 9 into blocks of sizes 1, 2, and 3?
So lets say I have [XXXXXXXXX]. How many ways can I 'fill' it with [X], [XX], and [XXX]
Some ways I could do it is:
[X][X][X][X][X][X][X][X][X] (9 1's)
[XX][XXX][X][XXX] (2-3-1-3)
Order matters, so one 3 followed by three 2's would be different from 3 2's then 1 3.

Let $A(n)$ be the number of ways to partition $n$ this way.  We have by hand count $A(1)=1,A(2)=2,A(3)=4$ and the recurrence $A(n)=A(n-1)+A(n-2)+A(n-3)$
