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A321253 Number of non-isomorphic strict connected weight-n multiset partitions with multiset density -1. 5
0, 1, 2, 5, 12, 28, 78, 202, 578, 1650, 4904 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 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(1) = 1 through a(5) = 28 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}}      {{1,1,2,2,2}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

CROSSREFS

Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A318697, A321155, A321194, A321228, A321229, A321254.

Sequence in context: A291234 A238828 A162036 * A290073 A232534 A274594

Adjacent sequences:  A321250 A321251 A321252 * A321254 A321255 A321256

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 01 2018

STATUS

approved

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Last modified July 22 16:39 EDT 2019. Contains 325224 sequences. (Running on oeis4.)