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A059585
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Number of labeled 3-node T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included).
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2
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0, 0, 12, 68, 235, 636, 1478, 3088, 5958, 10800, 18612, 30756, 49049, 75868, 114270, 168128, 242284, 342720, 476748, 653220, 882759, 1178012, 1553926, 2028048, 2620850, 3356080, 4261140, 5367492, 6711093, 8332860, 10279166, 12602368
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OFFSET
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0,3
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COMMENTS
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A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.
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LINKS
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Table of n, a(n) for n=0..31.
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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a(n) = binomial(n + 7, n) - 3*binomial(n + 3, n) + 2*binomial(n + 1, n) = n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040.
G.f.: x^2*(2-x)^2*(3-4*x+2*x^2)/(1-x)^8. [Colin Barker, Jun 25 2012]
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MAPLE
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for n from 0 to 100 do printf(`%d, `, n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040) od:
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CROSSREFS
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Cf. A059084, a(n)=A059584(n, 3), A059586.
Sequence in context: A199415 A200204 A200205 * A213547 A050484 A096425
Adjacent sequences: A059582 A059583 A059584 * A059586 A059587 A059588
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jan 23 2001
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EXTENSIONS
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More terms from James A. Sellers, Jan 24 2001
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STATUS
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approved
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