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A300913
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Number of non-isomorphic connected set-systems of weight n.
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55
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1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658, 1810, 5358, 16057, 50373, 161811, 536964, 1826151, 6380481, 22822280, 83587920, 312954111, 1197178941, 4674642341, 18620255306, 75606404857, 312763294254, 1317356836235, 5646694922172, 24618969819915, 109125629486233, 491554330852608
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OFFSET
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0,4
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COMMENTS
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The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.
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LINKS
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FORMULA
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Inverse Euler transform of A283877.
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EXAMPLE
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Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
1: {{1}}
2: {{1,2}}
3: {{1,2,3}}
{{2},{1,2}}
4: {{1,2,3,4}}
{{3},{1,2,3}}
{{1,3},{2,3}}
{{1},{2},{1,2}}
5: {{1,2,3,4,5}}
{{4},{1,2,3,4}}
{{1,4},{2,3,4}}
{{2,3},{1,2,3}}
{{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
{{3},{1,3},{2,3}}
Non-isomorphic representatives of the a(6) = 18 connected set-systems:
{{1,2,3,4,5,6}}
{{5},{1,2,3,4,5}}
{{1,5},{2,3,4,5}}
{{3,4},{1,2,3,4}}
{{1,2,5},{3,4,5}}
{{1,3,4},{2,3,4}}
{{1},{1,4},{2,3,4}}
{{1},{2,3},{1,2,3}}
{{3},{4},{1,2,3,4}}
{{3},{1,4},{2,3,4}}
{{3},{2,3},{1,2,3}}
{{4},{1,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,3},{2,3}}
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MATHEMATICA
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A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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