Don't have the notebook in front of me, but I did a 5^3 in the passenger seat and I think it went:
1, 3, 6, 10, 15, 18, 19, 18, 15, 10, 6, 3, 1
Somewhat interesting to note, if all 3 sites(n) rolled unique states(q), there are 6 combos; if one duplicate, 3; if triplets, 1. Didn't do a n=4...