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A321413 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons and relatively prime part sizes. 2
1, 0, 0, 0, 0, 3, 0, 14, 13, 50, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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, with relatively prime row sums (or column sums) and no row (or column) summing 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(5) = 3, a(7) = 14, and a(8) = 13 multiset partitions:

  {{11}{122}}  {{111}{1222}}    {{111}{11222}}

  {{11}{222}}  {{111}{2222}}    {{111}{22222}}

  {{12}{122}}  {{112}{1222}}    {{112}{12222}}

               {{11}{22222}}    {{122}{11222}}

               {{12}{12222}}    {{11}{122}{233}}

               {{122}{1122}}    {{11}{122}{333}}

               {{22}{11222}}    {{11}{222}{333}}

               {{11}{12}{233}}  {{11}{223}{233}}

               {{11}{22}{233}}  {{12}{122}{333}}

               {{11}{22}{333}}  {{12}{123}{233}}

               {{11}{23}{233}}  {{13}{112}{233}}

               {{12}{12}{333}}  {{13}{122}{233}}

               {{12}{13}{233}}  {{23}{123}{123}}

               {{13}{23}{123}}

CROSSREFS

Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616.

Cf. A320796, A320797, A320806, A320813, A321283, A321409, A321410, A321411.

Sequence in context: A008403 A138349 A323689 * A135399 A275831 A065121

Adjacent sequences:  A321410 A321411 A321412 * A321414 A321415 A321416

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 16 2018

STATUS

approved

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Last modified March 5 15:22 EST 2021. Contains 341825 sequences. (Running on oeis4.)