I think that Seth's last comment is on the right track.
For the two predicate case ("F" and "G"), each element in the universe can be placed either in the "F" and not "G" (and vice versa), in both, or in neither. We also know that any combination of simple monadic schema has a verifying universe with 2 or fewer elements since there are, at most, two existential generalizations. So there are 2^4 = 16 possible assignments. Since each interpretation of a schema must realize at least one of these assignments, there are 2^4 - 1 = 15 mutually exclusive interpretations. [Or, at least, this is according to my instructor, still trying to figure it out. Perhaps they are mutually dependent in some way?]
[This is where I get into guesswork.] There are 15 different interpretations, so find combinations of each of these interpretations for each possible number of verifying interpretations.
That is, use "15 choose r" for r from 0 to 15. This is a sum over r of 15!/[r!(15-r)!], which is symmetric.
When I do this I get a huge number (~60k), which makes me suspicious. Maybe there are duplicates in there?