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A330668 Number of non-isomorphic balanced reduced multisystems of weight n whose leaves (which are multisets of atoms) are all sets. 6
1, 1, 1, 3, 22, 204, 2953 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(4) = 22 multisystems:

  {1}  {1,2}  {1,2,3}      {1,2,3,4}

              {{1},{1,2}}  {{1},{1,2,3}}

              {{1},{2,3}}  {{1,2},{1,2}}

                           {{1,2},{1,3}}

                           {{1},{2,3,4}}

                           {{1,2},{3,4}}

                           {{1},{1},{1,2}}

                           {{1},{1},{2,3}}

                           {{1},{2},{1,2}}

                           {{1},{2},{1,3}}

                           {{1},{2},{3,4}}

                           {{{1}},{{1},{1,2}}}

                           {{{1}},{{1},{2,3}}}

                           {{{1,2}},{{1},{1}}}

                           {{{1}},{{2},{1,2}}}

                           {{{1,2}},{{1},{2}}}

                           {{{1}},{{2},{1,3}}}

                           {{{1,2}},{{1},{3}}}

                           {{{1}},{{2},{3,4}}}

                           {{{1,2}},{{3},{4}}}

                           {{{2}},{{1},{1,3}}}

                           {{{2,3}},{{1},{1}}}

CROSSREFS

The case with all atoms different is A318813.

The version where the leaves are multisets is A330474.

The tree version is A330626.

The maximum-depth case is A330677.

Unlabeled series-reduced rooted trees whose leaves are sets are A330624.

Cf. A000311, A004114, A005121, A005804, A007716, A048816, A141268, A283877, A306186, A318812, A320154, A330470, A330628, A330663.

Sequence in context: A098618 A207326 A006783 * A001409 A260154 A079489

Adjacent sequences:  A330665 A330666 A330667 * A330669 A330670 A330671

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 27 2019

STATUS

approved

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Last modified November 24 20:34 EST 2020. Contains 338616 sequences. (Running on oeis4.)