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

1,18

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.

Links

Table of n, a(n) for n=1..45.

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

Example

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

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}]

Crossrefs

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

Sequence in context: A128315 A198329 A123566 * A201757 A053390 A140643

Adjacent sequences: A279860 A279861 A279862 * A279864 A279865 A279866

Keyword

nonn

Author

Gus Wiseman, Dec 21 2016

Status

approved