This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319643 Number of non-isomorphic weight-n strict multiset partitions whose dual is an antichain of (not necessarily distinct) multisets. 1
 1, 1, 3, 6, 15, 29, 82, 179, 504, 1302, 3822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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. From Gus Wiseman, Aug 15 2019: (Start) Also the number of non-isomorphic T_0 weak antichains of weight n. The T_0 condition means that the dual is strict (no repeated edges). A weak antichain is a multiset of multisets, none of which is a proper submultiset of any other. For example, non-isomorphic representatives of the a(0) = 1 through a(4) = 15 T_0 weak antichains are:   {}  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}              {{1},{1}}  {{1,2,2}}      {{1,2,2,2}}              {{1},{2}}  {{1},{2,2}}    {{1,1},{1,1}}                         {{1},{1},{1}}  {{1,1},{2,2}}                         {{1},{2},{2}}  {{1},{2,2,2}}                         {{1},{2},{3}}  {{1,2},{2,2}}                                        {{1},{2,3,3}}                                        {{1,3},{2,3}}                                        {{1},{1},{2,2}}                                        {{1},{2},{3,3}}                                        {{1},{1},{1},{1}}                                        {{1},{1},{2},{2}}                                        {{1},{2},{2},{2}}                                        {{1},{2},{3},{3}}                                        {{1},{2},{3},{4}} (End) LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 multiset partitions: 1: {{1}} 2: {{1,1}}    {{1,2}}    {{1},{2}} 3: {{1,1,1}}    {{1,2,3}}    {{1},{1,1}}    {{1},{2,2}}    {{1},{2,3}}    {{1},{2},{3}} 4: {{1,1,1,1}}    {{1,1,2,2}}    {{1,2,3,4}}    {{1},{1,1,1}}    {{1},{1,2,2}}    {{1},{2,2,2}}    {{1},{2,3,4}}    {{1,1},{2,2}}    {{1,2},{3,3}}    {{1,2},{3,4}}    {{1},{2},{1,2}}    {{1},{2},{2,2}}    {{1},{2},{3,3}}    {{1},{2},{3,4}}    {{1},{2},{3},{4}} CROSSREFS Cf. A006126, A007716, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646. Cf. A245567, A293993, A319721, A326704, A326950, A326973, A326978. Sequence in context: A116696 A000220 A244705 * A092641 A077449 A152232 Adjacent sequences:  A319640 A319641 A319642 * A319644 A319645 A319646 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)