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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =6a(7) =21a(8) =42a(9) =112a(10) =252a(11) =378a(12) =759a(13) =1419a(14) =1914a(15) =3564a(16) =6864a(17) =9295a(18) =20020a(19) =45055a(20) =63083a(21) =146648a(22) =331568a(23) =456484a(24) =1007454a(25) =2156994a(26) =2896664a(27) =6165494a(28) =13079094a(29) =17441739