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A279863
Number of maximal transitive finitary sets with n brackets.
3
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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 21 2016
STATUS
approved