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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

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

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 October 23 12:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)