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A319286 Number of series-reduced locally disjoint rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n. 1
1, 2, 9, 67, 573, 6933, 97147, 1666999 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally disjoint if no branch overlaps any other branch of the same root.
LINKS
EXAMPLE
The a(3) = 9 trees:
(1(11))
(111)
(1(12))
(2(11))
(112)
(1(23))
(2(13))
(3(12))
(123)
Examples of rooted trees that are not locally disjoint are ((11)(12)) and ((12)(13)).
MATHEMATICA
disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
gro[m_]:=gro[m]=If[Length[m]==1, {m}, Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])], disjointQ]];
Table[Sum[Length[gro[m]], {m, Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]}], {n, 5}]
CROSSREFS
Sequence in context: A020555 A243281 A091795 * A158952 A324167 A296793
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)