Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= (n+2)/3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =3a(8) =18a(9) =24a(10) =84a(11) =224a(12) =280a(13) =630a(14) =1270a(15) =1527a(16) =2937a(17) =5742a(18) =6930a(19) =15015a(20) =35035a(21) =44044a(22) =108164a(23) =260064a(24) =328944a(25) =767244a(26) =1720944a(27) =2152710a(28) =4738410a(29) =10329750