6,6,6,6 = T4   = all possible ways to fill first 4 locations
6,1,1,6 = B1,4 = ways to violate C1 (after 4 locations)
6,5,1,1 = B2,4 = ways to violate C2 (but not C1)
          B3,4 = ways to maybe violate C3, never C1..C2
6,5,5,1 + A,B,C,C (maybe C = A)
6,1,5,1 + A,A,B,B
          B0,4 = T4 - B(1..3),4
          Let's enumerate these so we can check our work:
6,1,5,5 + A,A,B,C (maybe C = A)
6,5,1,5 + A,B,B,C
6,5,5,5 + A,B,C,D