A003467 Number of minimal covers of an n-set that cover exactly 3 points uniquely. (Formerly M3951)

5, 28, 190, 1340, 9065, 57512, 344316, 1966440, 10813935, 57672340, 299893594, 1526727748, 7633634645, 37580965520, 182536112120, 876173330832, 4161823312731, 19585050873180, 91396904062870, 423311976698380, 1947235092796609, 8901646138480568

Offset

3,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

T. Hearne and C. G. Wagner, Minimal covers of finite sets, Discr. Math. 5 (1973), 247-251.

Index entries for linear recurrences with constant coefficients, signature (20, -166, 740, -1921, 2960, -2656, 1280, -256).

Formula

G.f.: x^3*(1 + (1-4*x)^(-4) + 3*(1-x)^(-4)). - corrected by Vaclav Kotesovec, Oct 04 2012

Recurrence (for n>3): 4*(n-1)*n*a(n-2)-5*(n-4)*n*a(n-1)+(n-4)*(n-3)*a(n)=0. - Vaclav Kotesovec, Oct 04 2012

For n>3, a(n) = n*(n-1)*(n-2)*(4^n+192)/384. - Vaclav Kotesovec, Oct 26 2012

Mathematica

Table[SeriesCoefficient[x^3*(1+(1-4*x)^(-4)+3*(1-x)^(-4)), {x, 0, n}], {n, 3, 25}] (* Vaclav Kotesovec, Oct 04 2012 *)

Prog

(Magma) [5] cat [n*(n-1)*(n-2)*(4^n+192)/384: n in [4..30]]; // Vincenzo Librandi, May 03 2013

Crossrefs

Cf. A035347.

Sequence in context: A189487 A367049 A024065 * A240770 A318364 A064898

Adjacent sequences: A003464 A003465 A003466 * A003468 A003469 A003470

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name clarified by Geoffrey Critzer, Apr 23 2017

Status

approved