A324768 Number of fully anti-transitive rooted trees with n nodes.

1, 1, 2, 3, 6, 11, 27, 60, 152, 376, 968, 2492, 6549, 17259, 46000, 123214, 332304, 900406, 2451999, 6703925

Offset: 1

Author

Gus Wiseman, Mar 17 2019

Keywords

• nonn
• more

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.

Examples

			The a(1) = 1 through a(6) = 11 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, A279861, A290689, A304360, A306844, A318185.

Cf. A324695, A324751, A324756, A324758, A324763, A324765, A324769, A324770.

Cf. A324838, A324840, A324844, A324846.

Programs

Mathematica

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

Extensions

a(17)-a(20) from Jinyuan Wang, Jun 20 2020