Clebsch-Gordan Coefficients for three spin-1 particles?

[dipole]

I'm doing a problem where I need to know the coefficients to change from the
\vec{J} = \vec{J}_1 + \vec{J}_2 + \vec{J}_3 to the {\vec{J}_1, \vec{J}_2, \vec{J}_3} for three spin-1 particles, but I'm having trouble finding a table or reference for this... surely every time someone needs to write such a wave function they don't do all the algebra by hand, so where can I find a table to do this?

 

[vela]

You combine the angular momenta two at a time.

 

[dipole]

You combine the angular momenta two at a time.

This doesn't really help me...

For my situation, suppose I want to find all the states with m = 2. Well, there are three possibilities:

\mid j = 3, m =2 \rangle

and then two distinct states with \mid j = 2, m = 2 \rangle which correspond to a
symmetric and anti-symmetric state, presumably. How can I construct these by just coupling j_{12} with j_3 (where j_{12} is the coupled-states of j_1 and j_2)? How do I even start and how do I know which linear combinations to couple to which? It's very confusing. :(

 

[vela]

Well, give it a shot. There's no shortcut method if that's what you're looking for.