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%I #17 Jan 03 2024 15:06:13
%S 1,9,29,72,154,294,522,877,1406,2172,3255,4746,6763,9445,12953,17480,
%T 23254,30528,39604,50823,64568,81276,101443,125610,154395,188479,
%U 228611,275622,330432,394032,467524,552103,649064,759818,885901
%N Number of 3-covers of an unlabeled n-set.
%C Covers are defined in proper sense, i.e. without empty sets or multiple sets.
%H Andrew Howroyd, <a href="/A055195/b055195.txt">Table of n, a(n) for n = 2..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Covers</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1).
%F G.f.: x^2*(x^11-x^10-3*x^9+4*x^7+6*x^6-3*x^5-5*x^4-3*x^3+3*x^2+6*x+1)/((1-x^3)^2*(1-x^2)^2*(1-x)^3).
%t Drop[CoefficientList[Series[x^2(x^11-x^10-3x^9+4x^7+6x^6-3x^5-5x^4-3x^3+ 3x^2+6x+1)/ ((1-x^3)^2(1-x^2)^2(1-x)^3),{x,0,40}],x],2] (* or *) LinearRecurrence[ {3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1},{1,9,29,72,154,294,522,877,1406,2172,3255,4746,6763},40] (* _Harvey P. Dale_, Jul 18 2021 *)
%Y Column 3 of A055130.
%Y Cf. A005783.
%K nonn,easy
%O 2,2
%A _Vladeta Jovovic_, Jun 30 2000
%E More terms from _James A. Sellers_, Jul 04 2000
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