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A358454
Number of weakly transitive ordered rooted trees with n nodes.
3
1, 1, 1, 3, 6, 13, 33, 80, 201, 509, 1330, 3432, 8982, 23559, 62189
OFFSET
1,4
COMMENTS
We define an unlabeled ordered rooted tree to be weakly transitive if every branch of a branch of the root is itself a branch of the root.
EXAMPLE
The a(1) = 1 through a(6) = 13 trees:
o (o) (oo) (ooo) (oooo) (ooooo)
((o)o) ((o)oo) ((o)ooo)
(o(o)) ((oo)o) ((oo)oo)
(o(o)o) ((ooo)o)
(o(oo)) (o(o)oo)
(oo(o)) (o(oo)o)
(o(ooo))
(oo(o)o)
(oo(oo))
(ooo(o))
((o)(o)o)
((o)o(o))
(o(o)(o))
MATHEMATICA
aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n], Complement[Union@@#, #]=={}&]], {n, 10}]
CROSSREFS
The unordered version is A290689, ranked by A290822.
The directed version is A358453.
A000081 counts rooted trees.
A306844 counts anti-transitive rooted trees.
Sequence in context: A273974 A179928 A026538 * A372077 A361932 A201951
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 18 2022
STATUS
approved