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 A059585 Number of labeled 3-node T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1). FORMULA 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 MAPLE 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: MATHEMATICA CoefficientList[Series[x^2*(2 - x)^2*(3 - 4*x + 2*x^2)/(1 - x)^8, {x, 0, 50}], x] (* G. C. Greubel, Oct 06 2017 *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 12, 68, 235, 636, 1478, 3088}, 33] (* Vincenzo Librandi, Oct 07 2017 *) PROG (PARI) x='x+O('x^50); concat([0, 0], Vec(x^2*(2-x)^2*(3-4*x+2*x^2)/(1-x)^8)) \\ G. C. Greubel, Oct 06 2017 (Magma) [n*(n-1)*(n+1)*(n^4+28*n^3+323*n^2+1988*n+ 4572)/5040: n in [0..35]]; // Vincenzo Librandi, Oct 07 2017 CROSSREFS Cf. A059084, a(n)=A059584(n, 3), A059586. Sequence in context: A200204 A289384 A200205 * A213547 A050484 A359715 Adjacent sequences: A059582 A059583 A059584 * A059586 A059587 A059588 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Goran Kilibarda, Jan 23 2001 EXTENSIONS More terms from James A. Sellers, Jan 24 2001 STATUS approved

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Last modified September 9 16:40 EDT 2024. Contains 375765 sequences. (Running on oeis4.)