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A340600 Number of non-isomorphic balanced multiset partitions of weight n. 13
1, 1, 0, 4, 7, 16, 52, 206, 444, 1624, 5462 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

We define a multiset partition to be balanced if it has exactly as many parts as the greatest size of a part.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(5) = 16 multiset partitions (empty column indicated by dot):

  {{1}}  .  {{1},{1,1}}  {{1,1},{1,1}}  {{1},{1},{1,1,1}}

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

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

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

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

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

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

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

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

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

                                        {{1},{2},{3,4,5}}

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

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

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

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

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

CROSSREFS

The version for partitions is A047993.

The co-balanced version is A319616.

The cross-balanced version is A340651.

The twice-balanced version is A340652.

The version for factorizations is A340653.

A007716 counts non-isomorphic multiset partitions.

A007718 counts non-isomorphic connected multiset partitions.

A316980 counts non-isomorphic strict multiset partitions.

Other balance-related sequences:

- A098124 counts balanced compositions.

- A106529 lists balanced numbers.

- A340596 counts co-balanced factorizations.

- A340597 lists numbers with an alt-balanced factorization.

- A340598 counts balanced set partitions.

- A340599 counts alt-balanced factorizations.

Cf. A001055, A006141, A007717, A316983, A320663, A324522, A340654, A340655.

Sequence in context: A097661 A182561 A246915 * A013625 A182929 A124402

Adjacent sequences:  A340597 A340598 A340599 * A340601 A340602 A340603

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Feb 05 2021

STATUS

approved

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)