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A321401 Number of non-isomorphic strict self-dual multiset partitions of weight n. 5
1, 1, 2, 4, 7, 14, 29, 57, 117, 240, 498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 (or columns) are all different.

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}}.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

CROSSREFS

Cf. A000219, A007716, A045778, A059201, A316980, A316983, A319560, A319616.

Cf. A320796, A320797, A321402, A321405, A321406, A321407.

Sequence in context: A119268 A002989 A293336 * A000671 A199888 A157133

Adjacent sequences:  A321398 A321399 A321400 * A321402 A321403 A321404

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 09 2018

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)