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A324840
Number of fully recursively anti-transitive rooted trees with n nodes.
16
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.
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved