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A321404 Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons. 4
1, 0, 0, 0, 1, 0, 1, 1, 3, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Also the number of 0-1 symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which no row 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(4) = 1 through a(10) = 6 set multipartitions:

   4: {{1,2},{1,2}}

   6: {{1,2},{1,3},{2,3}}

   7: {{1,3},{2,3},{1,2,3}}

   8: {{2,3},{1,2,3},{1,2,3}}

   8: {{1,2},{1,2},{3,4},{3,4}}

   8: {{1,2},{1,3},{2,4},{3,4}}

   9: {{1,2,3},{1,2,3},{1,2,3}}

   9: {{1,2},{1,2},{3,4},{2,3,4}}

   9: {{1,2},{1,3},{1,4},{2,3,4}}

   9: {{1,2},{1,4},{3,4},{2,3,4}}

  10: {{1,2},{1,2},{1,3,4},{2,3,4}}

  10: {{1,2},{2,4},{1,3,4},{2,3,4}}

  10: {{1,3},{2,4},{1,3,4},{2,3,4}}

  10: {{1,4},{2,4},{3,4},{1,2,3,4}}

  10: {{1,2},{1,2},{3,4},{3,5},{4,5}}

  10: {{1,2},{1,3},{2,4},{3,5},{4,5}}

CROSSREFS

Cf. A007716, A049311, A135588, A138178, A283877, A302545, A316983.

Cf. A320797, A320798, A320811, A320812, A321403, A321404, A321405, A321406.

Sequence in context: A085841 A163483 A004784 * A024687 A072631 A085196

Adjacent sequences:  A321401 A321402 A321403 * A321405 A321406 A321407

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 15 2018

STATUS

approved

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)