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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)



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.


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


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}}





















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




Gus Wiseman, Dec 27 2019



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