A321679 Number of non-isomorphic weight-n antichains (not necessarily strict) of sets.

1, 1, 3, 5, 12, 19, 45, 75, 170, 314, 713

Offset

0,3

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.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(5) = 19 antichains:
  {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}        {{1,2,3,4,5}}
         {{1},{1}}  {{1},{2,3}}    {{1,2},{1,2}}      {{1},{2,3,4,5}}
         {{1},{2}}  {{1},{1},{1}}  {{1},{2,3,4}}      {{1,2},{3,4,5}}
                    {{1},{2},{2}}  {{1,2},{3,4}}      {{1,4},{2,3,4}}
                    {{1},{2},{3}}  {{1,3},{2,3}}      {{1},{1},{2,3,4}}
                                   {{1},{1},{2,3}}    {{1},{2,3},{2,3}}
                                   {{1},{2},{3,4}}    {{1},{2},{3,4,5}}
                                   {{1},{1},{1},{1}}  {{1},{2,3},{4,5}}
                                   {{1},{1},{2},{2}}  {{1},{2,4},{3,4}}
                                   {{1},{2},{2},{2}}  {{1},{1},{1},{2,3}}
                                   {{1},{2},{3},{3}}  {{1},{2},{2},{3,4}}
                                   {{1},{2},{3},{4}}  {{1},{2},{3},{4,5}}
                                                      {{1},{1},{1},{1},{1}}
                                                      {{1},{1},{2},{2},{2}}
                                                      {{1},{2},{2},{2},{2}}
                                                      {{1},{2},{2},{3},{3}}
                                                      {{1},{2},{3},{3},{3}}
                                                      {{1},{2},{3},{4},{4}}
                                                      {{1},{2},{3},{4},{5}}

Crossrefs

Cf. A006126, A049311, A096827, A285572, A293993, A293994, A318099, A319719, A319721, A320799, A321678.

Sequence in context: A341710 A024458 A143643 * A266819 A245939 A089292

Adjacent sequences: A321676 A321677 A321678 * A321680 A321681 A321682

Keyword

nonn,more

Author

Gus Wiseman, Nov 16 2018

Status

approved