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 A059945 Number of 4-block bicoverings of an n-set. 31
 0, 0, 4, 39, 280, 1815, 11284, 68859, 416560, 2509455, 15086764, 90610179, 543928840, 3264374295, 19588645444, 117539063499, 705255937120, 4231600258335, 25389795391324, 152339353740819, 914037866361400, 5484232429393575, 32905410268988404, 197432508689714139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. LINKS Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36). FORMULA a(n)=(1/4!)*(6^n-4*3^n-3*2^n+12). E.g.f. for m-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i=0..inf} x^i/i!*exp(binomial(i, 2)*y). a(0)=0, a(1)=0, a(2)=4, a(3)=39, a(n)=12*a(n-1)-47*a(n-2)+72*a(n-3)- 36*a(n-4) [From Harvey P. Dale, Aug 10 2011] G.f.: -x^3*(9*x-4) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). [Colin Barker, Jan 11 2013] EXAMPLE There are 4 4-block bicoverings of a 3-set: {{1},{2},{3},{1,2,3}}, {{2},{3},{1,2},{1,3}}, {{1},{3},{1,2},{2,3}} and {{1},{2},{1,3},{2,3}}. MATHEMATICA With[{c=1/4!}, Table[c(6^n-4 3^n-3 2^n+12), {n, 20}]] (* or *) LinearRecurrence[ {12, -47, 72, -36}, {0, 0, 4, 39}, 20] (* Harvey P. Dale, Aug 10 2011 *) CROSSREFS Cf. A002718, A059443, A003462, A059946-A059951. Sequence in context: A112460 A296594 A290559 * A198853 A093851 A224755 Adjacent sequences:  A059942 A059943 A059944 * A059946 A059947 A059948 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 14 2001 EXTENSIONS More terms from Colin Barker, Jan 11 2013 STATUS approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)