A279863 Number of maximal transitive finitary sets with n brackets.

0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 1, 1, 4, 3, 4, 2, 5, 6, 10, 8, 11, 11, 20, 22, 29, 36, 45, 53, 77, 83, 108, 141, 172, 208, 274, 323

Offset: 1

Author

Gus Wiseman, Dec 21 2016

Keywords

• nonn

Comments

A finitary set is transitive if every element is also a subset. A set system is maximal if the union is also a member.

Examples

			The a(23)=3 maximal transitive finitary sets are:
(()(())(()(()))((())(()(())))(()(())(()(())))),
(()(())((()))(((())))(()((())))(()(())((())))),
(()(())((()))(()(()))(()((())))(()(())((())))).
		

Links

• Gus Wiseman, Maximal transitive identity trees up to n=25

Crossrefs

Cf. A001192, A004111, A276625, A279065, A279614, A279861.

Programs

Mathematica

maxtransfins[n_]:=If[n===1,{},Select[Union@@FixedPointList[Complement[Union@@Function[fin,Cases[Complement[Subsets[fin],fin],sub_:>With[{nov=Sort[Append[fin,sub]]},nov/;Count[Union[nov,{Union@@nov}],_List,{0,Infinity}]<=n]]]/@#,#]&,{{}}],And[Count[#,_List,{0,Infinity}]===n,MemberQ[#,Union@@#]]&]];
Table[Length[maxtransfins[n]],{n,20}]