cp's OEIS Frontend

A324767 Number of recursively anti-transitive rooted identity trees with n nodes.

%I A324767 #7 Mar 18 2019 08:15:22
%S A324767 1,1,1,1,2,3,5,9,17,33,63,126,254,511,1039,2124,4371,9059,18839,39339,
%T A324767 82385,173111,364829,771010,1633313
%N A324767 Number of recursively anti-transitive rooted identity trees with n nodes.
%C A324767 An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of any terminal subtree is a branch of the same subtree. It is an identity tree if there are no repeated branches directly under a common root.
%C A324767 Also the number of finitary sets with n brackets where, at any level, no element of an element of a set is an element of the same set. For example, the a(8) = 9 finitary sets are (o = {}):
%C A324767   {{{{{{{o}}}}}}}
%C A324767   {{{{o,{{o}}}}}}
%C A324767   {{{o,{{{o}}}}}}
%C A324767   {{o,{{{{o}}}}}}
%C A324767   {{{o},{{{o}}}}}
%C A324767   {o,{{{{{o}}}}}}
%C A324767   {o,{{o,{{o}}}}}
%C A324767   {{o},{{{{o}}}}}
%C A324767   {{o},{o,{{o}}}}
%C A324767 The Matula-Goebel numbers of these trees are given by A324766.
%e A324767 The a(4) = 1 through a(8) = 9 recursively anti-transitive rooted identity trees:
%e A324767   (((o)))  (o((o)))   ((o((o))))   (((o((o)))))   ((o)(o((o))))
%e A324767            ((((o))))  (o(((o))))   ((o)(((o))))   (o((o((o)))))
%e A324767                       (((((o)))))  ((o(((o)))))   ((((o((o))))))
%e A324767                                    (o((((o)))))   (((o)(((o)))))
%e A324767                                    ((((((o))))))  (((o(((o))))))
%e A324767                                                   ((o)((((o)))))
%e A324767                                                   ((o((((o))))))
%e A324767                                                   (o(((((o))))))
%e A324767                                                   (((((((o)))))))
%t A324767 iallt[n_]:=Select[Union[Sort/@Join@@(Tuples[iallt/@#]&/@IntegerPartitions[n-1])],UnsameQ@@#&&Intersection[Union@@#,#]=={}&];
%t A324767 Table[Length[iallt[n]],{n,10}]
%Y A324767 Cf. A000081, A004111, A276625, A279861, A290689, A290760, A304360, A306844, A316500.
%Y A324767 Cf. A324695, A324751, A324758, A324764 (non-recursive version), A324765 (non-identity version), A324766, A324770, A324839, A324840, A324844.
%K A324767 nonn,more
%O A324767 1,5
%A A324767 _Gus Wiseman_, Mar 17 2019