login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330625 Number of series-reduced rooted trees whose leaves are sets (not necessarily disjoint) with multiset union a strongly normal multiset of size n. 8
1, 1, 3, 14, 123, 1330, 19694 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A rooted tree is series-reduced if it has no unary branchings, so every non-leaf node covers at least two other nodes.

A finite multiset is strongly normal if it covers an initial interval of positive integers with weakly decreasing multiplicities.

LINKS

Table of n, a(n) for n=0..6.

EXAMPLE

The a(1) = 1 through a(3) = 14 trees:

  {1}  {1,2}      {1,2,3}

       {{1},{1}}  {{1},{1,2}}

       {{1},{2}}  {{1},{2,3}}

                  {{2},{1,3}}

                  {{3},{1,2}}

                  {{1},{1},{1}}

                  {{1},{1},{2}}

                  {{1},{2},{3}}

                  {{1},{{1},{1}}}

                  {{1},{{1},{2}}}

                  {{1},{{2},{3}}}

                  {{2},{{1},{1}}}

                  {{2},{{1},{3}}}

                  {{3},{{1},{2}}}

MATHEMATICA

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]]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

srtrees[m_]:=Prepend[Join@@Table[Tuples[srtrees/@p], {p, Select[mps[m], Length[#1]>1&]}], m];

Table[Sum[Length[Select[srtrees[s], FreeQ[#, {___, x_Integer, x_Integer, ___}]&]], {s, strnorm[n]}], {n, 0, 5}]

CROSSREFS

The generalization where the leaves are multisets is A330467.

The singleton-reduced case is A330628.

The unlabeled version is A330624.

The case with all atoms distinct is A005804.

The case with all atoms equal is A196545.

The case where all leaves are singletons is A330471.

Cf. A000669, A004111, A141268, A300660, A316652, A330469, A330475, A330626, A330668, A330675.

Sequence in context: A127850 A324147 A186772 * A061029 A096657 A126933

Adjacent sequences:  A330622 A330623 A330624 * A330626 A330627 A330628

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 25 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 8 05:33 EDT 2020. Contains 335513 sequences. (Running on oeis4.)