A324840 Number of fully recursively anti-transitive rooted trees with n nodes.

1, 1, 2, 3, 5, 7, 14, 23, 46, 85, 165, 313, 625, 1225, 2459, 4919, 9928, 20078, 40926, 83592

Offset

1,3

Comments

An unlabeled rooted tree is fully recursively anti-transitive if no proper terminal subtree of any terminal subtree is a branch of the larger subtree.

Links

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

Gus Wiseman, The a(8) = 23 fully recursively anti-transitive rooted trees.

Gus Wiseman, The a(9) = 46 fully recursively anti-transitive rooted trees.

Gus Wiseman, The a(10) = 85 fully recursively anti-transitive rooted trees.

Example

The a(1) = 1 through a(7) = 14 fully recursively anti-transitive rooted trees:
  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)      (oooooo)
          ((o))  ((oo))   ((ooo))    ((oooo))     ((ooooo))
                 (((o)))  (((oo)))   (((ooo)))    (((oooo)))
                          ((o)(o))   ((o)(oo))    ((o)(ooo))
                          ((((o))))  ((((oo))))   ((oo)(oo))
                                     (((o)(o)))   ((((ooo))))
                                     (((((o)))))  (((o))(oo))
                                                  (((o)(oo)))
                                                  ((o)((oo)))
                                                  ((o)(o)(o))
                                                  (((((oo)))))
                                                  ((((o)(o))))
                                                  (((o))((o)))
                                                  ((((((o))))))

Mathematica

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

Crossrefs

Cf. A000081, A279861, A290689, A304360, A306844, A318185.

Cf. A324695, A324751, A324756, A324758, A324763, A324765, A324768, A324769, A324770.

Cf. A324838, A324841, A324844, A324846.

Sequence in context: A097799 A005629 A028304 * A316475 A303875 A331037

Adjacent sequences: A324837 A324838 A324839 * A324841 A324842 A324843

Keyword

nonn,more

Author

Gus Wiseman, Mar 17 2019

Status

approved