A324765 Number of recursively anti-transitive rooted trees with n nodes.

1, 1, 2, 3, 6, 11, 26, 52, 119, 266, 618, 1432, 3402, 8093, 19505, 47228, 115244, 282529, 696388, 1723400

Offset

1,3

Comments

An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of a terminal subtree is a branch of the same subtree.

Links

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

Example

The a(1) = 1 through a(6) = 11 recursively anti-transitive rooted trees:
  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)
          ((o))  ((oo))   ((ooo))    ((oooo))
                 (((o)))  (((oo)))   (((ooo)))
                          ((o)(o))   ((o)(oo))
                          (o((o)))   (o((oo)))
                          ((((o))))  (oo((o)))
                                     ((((oo))))
                                     (((o)(o)))
                                     ((o((o))))
                                     (o(((o))))
                                     (((((o)))))

Mathematica

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

Crossrefs

Cf. A000081, A290689, A301700, A304360, A306844, A317787, A318185.

Cf. A324695, A324751, A324756, A324758, A324764, A324766, A324767, A324768.

Cf. A324838, A324840, A324844.

Sequence in context: A107113 A156807 A032256 * A208602 A051603 A094927

Adjacent sequences: A324762 A324763 A324764 * A324766 A324767 A324768

Keyword

nonn,more

Author

Gus Wiseman, Mar 17 2019

Status

approved