A324770 Number of fully anti-transitive rooted identity trees with n nodes.

1, 1, 1, 1, 2, 3, 6, 13, 27, 58, 128, 286, 640, 1452, 3308, 7594, 17512, 40591, 94449, 220672

Offset

1,5

Comments

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.

Links

Table of n, a(n) for n=1..20.

Gus Wiseman, The a(11) = 128 fully anti-transitive rooted identity trees.

Example

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

Mathematica

idall[n_]:=If[n==1, {{}}, Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])], UnsameQ@@#&]];
Table[Length[Select[idall[n], Intersection[Union@@Rest[FixedPointList[Union@@#&, #]], #]=={}&]], {n, 10}]

Crossrefs

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

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

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

Sequence in context: A030038 A030040 A274493 * A075853 A132045 A032143

Adjacent sequences: A324767 A324768 A324769 * A324771 A324772 A324773

Keyword

nonn,more

Author

Gus Wiseman, Mar 17 2019

Status

approved