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A059945
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Number of 4-block bicoverings of an n-set.
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31
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0, 0, 4, 39, 280, 1815, 11284, 68859, 416560, 2509455, 15086764, 90610179, 543928840, 3264374295, 19588645444, 117539063499, 705255937120, 4231600258335, 25389795391324, 152339353740819
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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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]
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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}}.
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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] (* From Harvey P. Dale, Aug 10 2011 *)
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CROSSREFS
| Cf. A002718, A059443, A003462, A059946-A059951.
Sequence in context: A024212 A006408 A112460 * A198853 A093851 A063035
Adjacent sequences: A059942 A059943 A059944 * A059946 A059947 A059948
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 14 2001
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