~~Visualise the Manhattan distance as a cube in 3d space with axes R, G and B.~~

Then it's easy to permute the possibilities... It's the boundary of a cube of size 2n+1 for a distance n.

EDIT: Hint - you already worked out the vertices of the cube with manhattan distance 1, do the same with n to get the vertices of the cube of manhattan distance n, and fill in the square faces in a loop.

EDIT2: Ooops, no it's not, that's the answer for the max distance metric ;) The correct answer is a diamond with vertices at the points... sorry ;)

EDIT3: That's nearly as easy to visualise though. That's why there are 6 vertices, not 8 as well.