A319721 Number of non-isomorphic antichains of multisets of weight n.

1, 1, 4, 8, 24, 50, 148, 349, 1014, 2717, 8114

Offset: 0

Author

Gus Wiseman, Sep 26 2018

Keywords

• nonn
• more

Comments

In an antichain, no part is a proper submultiset of any other. The weight of an antichain is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 8 antichains:
1: {{1}}
2: {{1,1}}
   {{1,2}}
   {{1},{1}}
   {{1},{2}}
3: {{1,1,1}}
   {{1,2,2}}
   {{1,2,3}}
   {{1},{2,2}}
   {{1},{2,3}}
   {{1},{1},{1}}
   {{1},{2},{2}}
   {{1},{2},{3}}
		

Links

• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).

Crossrefs

Cf. A001055, A001970, A007716, A096827, A253249, A285572, A285573, A293993, A318099, A319616-A319646, A319719.