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

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

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A035347.

Programs

Magma

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

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 *)

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

Extensions

Name clarified by Geoffrey Critzer, Apr 23 2017