cp's OEIS Frontend

A279861 Number of transitive finitary sets with n brackets. Number of transitive rooted identity trees with n nodes.

%I A279861 #7 Dec 21 2016 11:06:03
%S A279861 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,
%T A279861 158,199,277,376,505,684,934,1241,1711,2300,3123,4236,5763,7814,10647,
%U A279861 14456,19662
%N A279861 Number of transitive finitary sets with n brackets. Number of transitive rooted identity trees with n nodes.
%C A279861 A finitary set is transitive if every element is also a subset. Transitive sets are also called full sets.
%H A279861 Wikipedia, <a href="https://en.wikipedia.org/wiki/Transitive_set">Transitive set</a>
%H A279861 Gus Wiseman, <a href="/A279861/a279861.png">Transitive rooted identity trees example n=23</a>
%e A279861 Sequence of transitive finitary sets begins:
%e A279861 1  ()
%e A279861 2  (())
%e A279861 4  (()(()))
%e A279861 7  (()(())((())))
%e A279861 8  (()(())(()(())))
%e A279861 11 (()(())((()))(((()))))
%e A279861    (()(())((()))(()(())))
%e A279861 12 (()(())((()))(()((()))))
%e A279861 13 (()(())((()))((())((()))))
%e A279861    (()(())(()(()))((()(()))))
%e A279861 14 (()(())((()))(()(())((()))))
%e A279861    (()(())(()(()))(()(()(()))))
%e A279861 15 (()(())((()))(((())))(()(())))
%e A279861    (()(())(()(()))((())(()(()))))
%e A279861 16 (()(())((()))(((())))((((())))))
%e A279861    (()(())((()))(((())))(()((()))))
%e A279861    (()(())((()))(()(()))(()((()))))
%e A279861    (()(())((()))(()(()))((()(()))))
%e A279861    (()(())(()(()))(()(())(()(()))))
%e A279861 17 (()(())((()))(((())))(()(((())))))
%e A279861    (()(())((()))(((())))((())((()))))
%e A279861    (()(())((()))(()(()))(()(()(()))))
%e A279861    (()(())((()))(()(()))((())((()))))
%e A279861 18 (()(())((()))(((())))((())(((())))))
%e A279861    (()(())((()))(((())))(()(())((()))))
%e A279861    (()(())((()))(()(()))((())(()(()))))
%e A279861    (()(())((()))(()(()))(()(())((()))))
%e A279861    (()(())((()))((()((()))))(()((()))))
%e A279861    (()(())((()))(()((())))((())((()))))
%t A279861 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&]];
%t A279861 Table[Length[transfins[n]],{n,20}]
%Y A279861 Cf. A001192, A004111, A061773, A279614, A276625, A279065, A279863.
%K A279861 nonn
%O A279861 1,11
%A A279861 _Gus Wiseman_, Dec 21 2016