a(n) = size of the n-th term in S(10) (defined in Comments).

Terms

a(0) =4a(1) =21a(2) =143a(3) =1061a(4) =8363a(5) =68900a(6) =1a(7) =1a(8) =1a(9) =1a(10) =1a(11) =1a(12) =586044a(13) =1a(14) =1a(15) =1a(16) =1a(17) =1a(18) =1a(19) =1a(20) =1a(21) =1a(22) =1a(23) =1a(24) =1a(25) =1a(26) =1a(27) =1a(28) =1a(29) =1