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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 18 2022
STATUS
approved