A319645 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of distinct multisets.

1, 1, 1, 2, 3, 4, 7, 9, 16, 22, 38

Offset

0,4

Comments

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. 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.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(6) = 7 antichains:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
   {{1,2,2}}
4: {{1,1,1,1}}
   {{1,2,2,2}}
   {{1,2},{2,2}}
5: {{1,1,1,1,1}}
   {{1,1,2,2,2}}
   {{1,2,2,2,2}}
   {{1,2},{2,2,2}}
6: {{1,1,1,1,1,1}}
   {{1,1,2,2,2,2}}
   {{1,2,2,2,2,2}}
   {{1,2,2,3,3,3}}
   {{1,2},{2,2,2,2}}
   {{1,2,2},{2,2,2}}
   {{1,2,3},{2,3,3}}

Crossrefs

Cf. A000219, A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319616-A319646.

Sequence in context: A250255 A070763 A295619 * A071114 A078696 A256772

Adjacent sequences: A319642 A319643 A319644 * A319646 A319647 A319648

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved