A321402 Number of non-isomorphic strict self-dual multiset partitions of weight n with no singletons.

1, 0, 1, 1, 2, 4, 8, 14, 27, 53, 105

Offset

0,5

Comments

Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows are all different and none sums to 1.

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

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

Example

Non-isomorphic representatives of the a(2) = 1 through a(7) = 14 multiset partitions:
  {{11}}  {{111}}  {{1111}}    {{11111}}    {{111111}}      {{1111111}}
                   {{11}{22}}  {{11}{122}}  {{111}{222}}    {{111}{1222}}
                               {{11}{222}}  {{112}{122}}    {{111}{2222}}
                               {{12}{122}}  {{11}{2222}}    {{112}{1222}}
                                            {{12}{1222}}    {{11}{22222}}
                                            {{22}{1122}}    {{12}{12222}}
                                            {{11}{22}{33}}  {{122}{1122}}
                                            {{12}{13}{23}}  {{22}{11222}}
                                                            {{11}{12}{233}}
                                                            {{11}{22}{233}}
                                                            {{11}{22}{333}}
                                                            {{11}{23}{233}}
                                                            {{12}{13}{233}}
                                                            {{13}{23}{123}}

Crossrefs

Cf. A000219, A007716, A059201, A302545, A316980, A316983, A319560, A319616.

Cf. A320796, A320797, A320798, A320804, A320811, A320812, A321401, A321404, A321405, A321406, A321407.

Sequence in context: A214255 A065616 A164147 * A210669 A122026 A196721

Adjacent sequences: A321399 A321400 A321401 * A321403 A321404 A321405

Keyword

nonn,more

Author

Gus Wiseman, Nov 09 2018

Status

approved