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A358460
Number of locally disjoint ordered rooted trees with n nodes.
1
1, 1, 2, 5, 13, 36, 103, 301, 902, 2767, 8637, 27324, 87409, 282319, 919352
OFFSET
1,3
COMMENTS
Locally disjoint means no branch of any vertex overlaps a different (unequal) branch of the same vertex.
EXAMPLE
The a(1) = 1 through a(5) = 13 trees:
o (o) (oo) (ooo) (oooo)
((o)) ((o)o) ((o)oo)
((oo)) ((oo)o)
(o(o)) ((ooo))
(((o))) (o(o)o)
(o(oo))
(oo(o))
(((o))o)
(((o)o))
(((oo)))
((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], FreeQ[#, {___, {___, x_, ___}, ___, {___, x_, ___}, ___}]&]], {n, 10}]
CROSSREFS
The locally non-intersecting version is A143363, unordered A007562.
The unordered version is A316473, ranked by A316495.
A000108 counts ordered rooted trees, unordered A000081.
A358453 counts transitive ordered trees, unordered A290689.
Sequence in context: A277996 A370168 A099164 * A289453 A339290 A036765
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 19 2022
STATUS
approved