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%I M3951 #39 Oct 21 2023 18:39:13
%S 5,28,190,1340,9065,57512,344316,1966440,10813935,57672340,299893594,
%T 1526727748,7633634645,37580965520,182536112120,876173330832,
%U 4161823312731,19585050873180,91396904062870,423311976698380,1947235092796609,8901646138480568
%N Number of minimal covers of an n-set that cover exactly 3 points uniquely.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003467/b003467.txt">Table of n, a(n) for n = 3..1000</a>
%H T. Hearne and C. G. Wagner, <a href="http://dx.doi.org/10.1016/0012-365X(73)90141-6">Minimal covers of finite sets</a>, Discr. Math. 5 (1973), 247-251.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (20, -166, 740, -1921, 2960, -2656, 1280, -256).
%F G.f.: x^3*(1 + (1-4*x)^(-4) + 3*(1-x)^(-4)). - corrected by _Vaclav Kotesovec_, Oct 04 2012
%F 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
%F For n>3, a(n) = n*(n-1)*(n-2)*(4^n+192)/384. - _Vaclav Kotesovec_, Oct 26 2012
%t Table[SeriesCoefficient[x^3*(1+(1-4*x)^(-4)+3*(1-x)^(-4)),{x,0,n}],{n,3,25}] (* _Vaclav Kotesovec_, Oct 04 2012 *)
%o (Magma) [5] cat [n*(n-1)*(n-2)*(4^n+192)/384: n in [4..30]]; // _Vincenzo Librandi_, May 03 2013
%Y Cf. A035347.
%K nonn,easy
%O 3,1
%A _N. J. A. Sloane_
%E Name clarified by _Geoffrey Critzer_, Apr 23 2017
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