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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

Table of n, a(n) for n=1..24.

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.)