%I M2790 #47 Feb 28 2023 21:09:35
%S 1,3,9,23,51,103,196,348,590,960,1506,2290,3393,4905,6945,9651,13185,
%T 17739,23542,30846,39954,51206,64986,81730,101935,126141,154967,
%U 189093,229269,276325,331182,394830,468372,553002,650016,760824,886963
%N Number of 3-covers of an unlabeled n-set.
%C Equals first differences of A002727. - _Vladeta Jovovic_, May 24 2000
%C Number of 3 X n binary matrices with at least one 1 in every column up to row and column permutations. - _Andrew Howroyd_, Feb 28 2023
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Stefano Spezia, <a href="/A005783/b005783.txt">Table of n, a(n) for n = 0..10000</a> (terms for n = 1..1000 from T. D. Noe)
%H R. J. Clarke, <a href="http://dx.doi.org/10.1016/0012-365X(90)90146-9">Covering a set by subsets</a>, Discrete Math., 81 (1990), 147-152.
%H Masaaki Harada, Ken Saito, <a href="https://arxiv.org/abs/1802.06985">Binary linear complementary dual codes</a>, arXiv:1802.06985 [math.CO], 2018.
%H Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</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^6+x^4+2*x^3+x^2+1)/((1-x^3)^2*(1-x^2)^2*(1-x)^3).
%F a(n) ~ n^6/4320. - _Stefano Spezia_, Aug 08 2022
%F a(n) = n^6/4320 + 7*n^5/1440 + 79*n^4/1728 + 35*n^3/144 + 2939*n^2/4320 + 8863*n/8640 + 1 + (n/16 + 7/32)*floor(n/2) + (n/9 + 11/27)*floor(n/3) + floor((n+1)/3)/27. - _Vaclav Kotesovec_, Aug 09 2022
%t CoefficientList[Series[(x^6+x^4+2x^3+x^2+1)/((1-x^3)^2(1-x^2)^2 (1-x)^3),{x,0,50}],x] (* _Harvey P. Dale_, May 19 2011 *)
%o (PARI) Vec(G(3, x)*(1 - x) + O(x^40)) \\ G defined in A028657. - _Andrew Howroyd_, Feb 28 2023
%Y Column 3 of A055080.
%Y Cf. A002727, A002620, A005784, A005785, A005786, A055066.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, May 24 2000
%E a(0) = 1 prepended by _Stefano Spezia_, Aug 09 2022