%I M3535 #43 Feb 28 2023 21:09:31
%S 1,4,17,65,230,736,2197,6093,15864,38960,90837,202005,430577,883057,
%T 1748909,3355213,6252575,11345602,20089514,34778306,58964020,98053576,
%U 160151566,257229974,406739271,633795181,974126408,1477999320,2215409037,3282874359,4812278064
%N Number of 4-covers of an unlabeled n-set.
%C Number of 4 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="/A005784/b005784.txt">Table of n, a(n) for n = 0..10000</a>
%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 Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</a>
%H <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (5, -7, -1, 5, -1, 21, -33, 0, -4, 8, 68, -57, -3, -57, 13, 100, -32, 32, -100, -13, 57, 3, 57, -68, -8, 4, 0, 33, -21, 1, -5, 1, 7, -5, 1).
%F G.f.: (x^20 - x^19 + 4*x^18 + 9*x^17 + 23*x^16 + 39*x^15 + 90*x^14 + 131*x^13 + 204*x^12 + 238*x^11 + 252*x^10 + 238*x^9 + 204*x^8 + 131*x^7 + 90*x^6 + 39*x^5 + 23*x^4 + 9*x^3 + 4*x^2 - x + 1)/((1 - x^4)^3*(1 - x^3)^4*(1 - x^2)^3*(1 - x)^5).
%F a(n) ~ n^14/2092278988800. - _Stefano Spezia_, Aug 08 2022
%F a(n) = n^14/2092278988800 + n^13/19926466560 + n^12/418037760 + n^11/14598144 + 689*n^10/522547200 + 253*n^9/13934592 + 2184839*n^8/11705057280 + 10313*n^7/6967296 + 2319707*n^6/250822656 + 1817221*n^5/39813120 + 2405336243*n^4/13795246080 + 151784975*n^3/306561024 + 93746545019*n^2/95103590400 + 924100468541*n/717352796160 + 1 + (n^2/486 + 5*n/162 + 233/2187)*floor(n/3) + (n^2/256 + 15*n/256 + 101/512)*floor(n/4) - (n^3/1458 + 7*n^2/486 + 22*n/243 + 356/2187)*floor((n+1)/3) + (n^5/122880 + 5*n^4/16384 + 125*n^3/24576 + 359*n^2/8192 + 10967*n/61440 + 8461/32768)*floor(n/2) + (n/256 + 15/512)*floor((n+1)/4). - _Vaclav Kotesovec_, Aug 09 2022
%o (PARI) Vec(G(4, x)*(1 - x) + O(x^40)) \\ G defined in A028657. - _Andrew Howroyd_, Feb 28 2023
%Y Column 4 of A055080.
%Y First differences of A006148.
%Y Cf. A002620, A005783, A005785, A005786, A055066.
%K easy,nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Jun 03 2000
%E a(0)=1 prepended by _Alois P. Heinz_, Aug 08 2022