Given that most games today start with a move in each of the 4 corner at either 4-4 or 3-4 I wanted to compute how many possibilities there are. Without taking symmetry into account there are 4! * 3^4 = 972 possibilities. With symmetry ...

I approached this by thinking about the topology first then the coloring

Star points only: one topology (4 2) colorings 3 symmetries = 2
One 3-4: one topology, (4 2) colorings, no symmetry = 6
...

In a first, less mathematical approach, I got to 69. I'll complete this here but maybe someone has done the math already or is faster than me.

And I have sgf files for them: 4m_symm_without33 in https://github.com/isty2e/baduk-opening-book