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

Author

Gus Wiseman, Mar 17 2019

Keywords

• nonn
• more

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.

Examples

			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)))))
		

Crossrefs

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

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

Cf. A324838, A324840, A324844.

Programs

Mathematica

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