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 A056078 Number of proper T_1-hypergraphs with 3 labeled nodes and n hyperedges. 2
 0, 0, 2, 15, 54, 141, 306, 588, 1036, 1710, 2682, 4037, 5874, 8307, 11466, 15498, 20568, 26860, 34578, 43947, 55214, 68649, 84546, 103224, 125028, 150330, 179530, 213057, 251370, 294959, 344346, 400086, 462768, 533016, 611490, 698887, 795942, 903429, 1022162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also number of 3 X 3 matrices with nonnegative integer entries with zero main diagonal and without zero rows or columns, such that sum of all entries is n. - Vladeta Jovovic, Sep 06 2006 A T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v. A proper hypergraph is a hypergraph without empty hyperedges or hyperedges containing all nodes. - Vladeta Jovovic, Sep 06 2006 REFERENCES V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6) V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = C(n+5,5) -6*C(n+3,3) +6*C(n+2,2) +3*C(n+1,1) -6*C(n,0). a(n+1) = ( n^4 +20*n^3 +35*n^2 -140*n +84 )*n/120. From Colin Barker, Jul 11 2013: (Start) a(n) = (-240+394*n-135*n^2-35*n^3+15*n^4+n^5)/120. G.f.: x^3 *(x-2) *(2*x^2-2*x-1) / (x-1)^6. (End) EXAMPLE There are 15 proper T_1-hypergraphs with 3 nodes and 4 hyperedges: {{3},{3},{2},{1}}, {{3},{2},{2},{1}}, {{3},{2},{2,3},{1}}, {{3},{2},{1},{1}}, {{3},{2},{1},{1,3}}, {{3},{2},{1},{1,2}}, {{3},{2},{1,3},{1,2}}, {{3},{2,3},{1},{1,2}}, {{3},{2,3},{1,3},{1,2}}, {{2},{2,3},{1},{1,3}}, {{2},{2,3},{1,3},{1,2}}, {{2,3},{2,3},{1,3},{1,2}}, {{2,3},{1},{1,3},{1,2}}, {{2,3},{1,3},{1,3},{1,2}}, {{2,3},{1,3},{1,2},{1,2}}. MATHEMATICA Table[(n^4 + 20*n^3 + 35*n^2 - 140*n + 84)*n/120, {n, 0, 50}] (* G. C. Greubel, Oct 07 2017 *) PROG (PARI) for(n=0, 25, print1((n^4 + 20*n^3 + 35*n^2 - 140*n + 84)*n/120, ", ")) \\ G. C. Greubel, Oct 07 2017 (Magma) [(n^4 + 20*n^3 + 35*n^2 - 140*n + 84)*n/120: n in [0..25]]; // G. C. Greubel, Oct 07 2017 CROSSREFS Cf. A056005, A047707. Sequence in context: A015520 A098520 A216333 * A142861 A305673 A268761 Adjacent sequences: A056075 A056076 A056077 * A056079 A056080 A056081 KEYWORD nonn,easy AUTHOR Vladeta Jovovic, Goran Kilibarda, Jul 26 2000 EXTENSIONS More terms from Colin Barker, Jul 11 2013 STATUS approved

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Last modified February 3 01:46 EST 2023. Contains 360024 sequences. (Running on oeis4.)