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A319719
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Number of non-isomorphic connected antichains of multisets of weight n.
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24
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1, 1, 3, 4, 10, 14, 48, 95, 305, 822, 2615
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OFFSET
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0,3
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COMMENTS
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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. Connected antichains are also called clutters.
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LINKS
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Table of n, a(n) for n=0..10.
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).
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EXAMPLE
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Non-isomorphic representatives of the a(1) = 1 through a(4) = 10 connected antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1,1},{1,1}}
{{1,2},{1,2}}
{{1,2},{2,2}}
{{1,3},{2,3}}
{{1},{1},{1},{1}}
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CROSSREFS
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Cf. A001055, A001970, A007716, A007718, A056156, A096827, A253249, A285573, A293994, A318099, A319557, A319616-A319646, A319721.
Sequence in context: A056516 A056517 A285042 * A347568 A048155 A242342
Adjacent sequences: A319716 A319717 A319718 * A319720 A319721 A319722
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Sep 26 2018
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STATUS
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approved
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