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 A279861 Number of transitive finitary sets with n brackets. Number of transitive rooted identity trees with n nodes. 26
 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 2, 2, 5, 4, 6, 8, 10, 14, 23, 26, 34, 46, 64, 81, 115, 158, 199, 277, 376, 505, 684, 934, 1241, 1711, 2300, 3123, 4236, 5763, 7814, 10647, 14456, 19662 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS A finitary set is transitive if every element is also a subset. Transitive sets are also called full sets. LINKS Wikipedia, Transitive set Gus Wiseman, Transitive rooted identity trees example n=23 EXAMPLE Sequence of transitive finitary sets begins: 1  () 2  (()) 4  (()(())) 7  (()(())((()))) 8  (()(())(()(()))) 11 (()(())((()))(((()))))    (()(())((()))(()(()))) 12 (()(())((()))(()((())))) 13 (()(())((()))((())((()))))    (()(())(()(()))((()(())))) 14 (()(())((()))(()(())((()))))    (()(())(()(()))(()(()(())))) 15 (()(())((()))(((())))(()(())))    (()(())(()(()))((())(()(())))) 16 (()(())((()))(((())))((((())))))    (()(())((()))(((())))(()((()))))    (()(())((()))(()(()))(()((()))))    (()(())((()))(()(()))((()(()))))    (()(())(()(()))(()(())(()(())))) 17 (()(())((()))(((())))(()(((())))))    (()(())((()))(((())))((())((()))))    (()(())((()))(()(()))(()(()(()))))    (()(())((()))(()(()))((())((())))) 18 (()(())((()))(((())))((())(((())))))    (()(())((()))(((())))(()(())((()))))    (()(())((()))(()(()))((())(()(()))))    (()(())((()))(()(()))(()(())((()))))    (()(())((()))((()((()))))(()((()))))    (()(())((()))(()((())))((())((())))) MATHEMATICA transfins[n_]:=transfins[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[nov, _List, {0, Infinity}]<=n]]]/@#, #]&, Array[transfins, n-1, 1, Union]], Count[#, _List, {0, Infinity}]===n&]]; Table[Length[transfins[n]], {n, 20}] CROSSREFS Cf. A001192, A004111, A061773, A279614, A276625, A279065, A279863. Sequence in context: A285442 A108115 A089254 * A321431 A140085 A071445 Adjacent sequences:  A279858 A279859 A279860 * A279862 A279863 A279864 KEYWORD nonn AUTHOR Gus Wiseman, Dec 21 2016 STATUS approved

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Last modified May 31 21:42 EDT 2020. Contains 334748 sequences. (Running on oeis4.)