%I M4156 #22 Feb 28 2023 22:25:19
%S 1,6,23,65,156,336,664,1229,2159,3629,5877,9221,14070,20951,30530,
%T 43634,61283,84725,115461,155294,206368,271210,352784,454550,580509,
%U 735280,924163,1153207,1429292,1760218,2154776,2622859,3175555,3825247
%N Number of n-covers of an unlabeled 3-set.
%C Number of n X 3 binary matrices with at least one 1 in every column up to row and column permutations. - _Andrew Howroyd_, Feb 28 2023
%D R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A005745/b005745.txt">Table of n, a(n) for n = 1..1000</a>
%H Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</a>
%F a(n) = A002727(n) - A002623(n).
%F G.f.: -x*(x^8-x^7-x^6-2*x^5+2*x^4+x^3-3*x^2-2*x-1)/((x^3-1)^2*(x^2-1)^2*(x-1)^4).
%o (PARI) Vec(G(3, x) - G(2, x) + O(x^40)) \\ G defined in A028657. - _Andrew Howroyd_, Feb 28 2023
%Y A diagonal of A055080.
%Y First differences give A055609.
%Y Cf. A002623, A002727.
%Y Cf. A005744, A005746, A005747, A005748, A005771.
%K easy,nonn
%O 1,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _Vladeta Jovovic_, May 26 2000