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A320798 Number of non-isomorphic weight-n connected antichains of non-constant multisets with multiset density -1. 7
0, 1, 2, 5, 9, 24, 51, 134, 328, 868 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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=1..10.

EXAMPLE

Non-isomorphic representatives of the a(2) = 1 through a(6) = 24 multiset partitions:

  {{12}}  {{122}}  {{1122}}    {{11222}}    {{111222}}

          {{123}}  {{1222}}    {{12222}}    {{112222}}

                   {{1233}}    {{12233}}    {{112233}}

                   {{1234}}    {{12333}}    {{122222}}

                   {{13}{23}}  {{12344}}    {{122333}}

                               {{12345}}    {{123333}}

                               {{12}{233}}  {{123344}}

                               {{13}{233}}  {{123444}}

                               {{14}{234}}  {{123455}}

                                            {{123456}}

                                            {{112}{233}}

                                            {{122}{233}}

                                            {{12}{2333}}

                                            {{123}{344}}

                                            {{124}{344}}

                                            {{125}{345}}

                                            {{13}{2233}}

                                            {{13}{2333}}

                                            {{13}{2344}}

                                            {{133}{233}}

                                            {{14}{2344}}

                                            {{15}{2345}}

                                            {{13}{24}{34}}

                                            {{14}{24}{34}}

CROSSREFS

Cf. A007716, A007718, A286520, A304867, A319719, A319721, A321155, A321760, A322111, A322113.

Sequence in context: A075200 A075198 A294633 * A006405 A305189 A243559

Adjacent sequences:  A320795 A320796 A320797 * A320799 A320800 A320801

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 29 2018

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)