A324770 - OEIS

%I #4 Mar 18 2019 08:15:46

%S 1,1,1,1,2,3,6,13,27,58,128,286,640,1452,3308,7594,17512,40591,94449,

%T 220672

%N Number of fully anti-transitive rooted identity trees with n nodes.

%C An unlabeled rooted tree is fully anti-transitive if no proper terminal subtree of any branch of the root is a branch of the root. It is an identity tree if there are no repeated branches directly under the same root.

%H Gus Wiseman, <a href="/A324770/a324770.png">The a(11) = 128 fully anti-transitive rooted identity trees</a>.

%e The a(1) = 1 through a(7) = 6 fully anti-transitive rooted identity trees:

%e   o  (o)  ((o))  (((o)))  ((o(o)))   (((o(o))))   ((o(o(o))))

%e                           ((((o))))  ((o((o))))   ((((o(o)))))

%e                                      (((((o)))))  (((o)((o))))

%e                                                   (((o((o)))))

%e                                                   ((o(((o)))))

%e                                                   ((((((o))))))

%t idall[n_]:=If[n==1,{{}},Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])],UnsameQ@@#&]];

%t Table[Length[Select[idall[n],Intersection[Union@@Rest[FixedPointList[Union@@#&,#]],#]=={}&]],{n,10}]

%Y Cf. A000081, A004111, A276625, A279861, A290760, A304360, A306844.

%Y Cf. A324695, A324751, A324763, A324764, A324765, A324767, A324769.

%Y Cf. A324839, A324840, A324843, A324844, A324846.

%K nonn,more

%O 1,5

%A _Gus Wiseman_, Mar 17 2019