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A319721 Number of non-isomorphic antichains of multisets of weight n. 34
1, 1, 4, 8, 24, 50, 148, 349, 1014, 2717, 8114 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

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

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

EXAMPLE

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}}

CROSSREFS

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

Sequence in context: A266821 A306484 A208901 * A115641 A153334 A116719

Adjacent sequences:  A319718 A319719 A319720 * A319722 A319723 A319724

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 26 2018

STATUS

approved

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Last modified October 19 12:10 EDT 2019. Contains 328219 sequences. (Running on oeis4.)