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A322112 Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1. 1
1, 0, 1, 1, 1, 2, 2, 4, 4, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.

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}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.

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(10) = 9 multiset partitions:

  {{11}}  {{111}}  {{1111}}  {{11111}}    {{111111}}    {{1111111}}

                             {{11}{122}}  {{22}{1122}}  {{111}{1222}}

                                                        {{22}{11222}}

                                                        {{11}{12}{233}}

.

  {{11111111}}      {{111111111}}        {{1111111111}}

  {{111}{11222}}    {{1111}{12222}}      {{1111}{112222}}

  {{22}{112222}}    {{22}{1122222}}      {{22}{11222222}}

  {{11}{122}{233}}  {{222}{111222}}      {{222}{1112222}}

                    {{11}{11}{12233}}    {{111}{122}{2333}}

                    {{11}{113}{2233}}    {{22}{113}{23333}}

                    {{12}{111}{2333}}    {{22}{1133}{2233}}

                    {{22}{113}{2333}}    {{33}{33}{112233}}

                    {{12}{13}{22}{344}}  {{11}{14}{223}{344}}

CROSSREFS

Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A316983, A321155, A321255, A322111.

Sequence in context: A288045 A292941 A074818 * A324409 A110199 A222736

Adjacent sequences:  A322109 A322110 A322111 * A322113 A322114 A322115

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 26 2018

STATUS

approved

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Last modified August 6 15:50 EDT 2020. Contains 336255 sequences. (Running on oeis4.)