Assume all mixtures involve colors mixed in equal amounts and base colors are already on the palette. How many ways are there of mixing k distinct colors on a paint palette where each color must be mixed with at least one other color. For example $k=3$ would have a 3 way mix, 1 mixed into 2 others, and each mixed into each of the others separately. For 4 colors there are 10 such ways. These ways of mixing can be though of as the orbits formed by the permutation of colors acting on all mixtures of k particular colors following the above restrictions. I want to count the number of these orbits.
This would be a lot less than the number of 'unique palettes by color-list' which I believe is $2^{2^{k}-k-1}$.