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%I #23 Dec 09 2017 10:41:26
%S 0,0,0,2,56,790,8380,76482,638736,5043950,38390660,285007162,
%T 2079779416,14995363110,107204473740,761823557042,5390550296096,
%U 38026057186270,267656481977620,1881017836414122,13204444871932776,92618543463601430,649270263511862300
%N Number of 3-antichain covers of a labeled n-set.
%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H G. C. Greubel, <a href="/A056046/b056046.txt">Table of n, a(n) for n = 0..1000</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (22,-190,820,-1849,2038,-840).
%F a(n) = (1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2).
%F G.f.: -2*x^3*(31*x^2-6*x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - _Colin Barker_, Nov 27 2012
%e There are 2 3-antichain covers of a labeled 3-set: {{1},{2},{3}}, {{1,2},{1,3},{2,3}}.
%t Table[(1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2), {n, 0, 50}] (* _G. C. Greubel_, Oct 06 2017 *)
%t LinearRecurrence[{22,-190,820,-1849,2038,-840},{0,0,0,2,56,790},30] (* _Harvey P. Dale_, Dec 09 2017 *)
%o (PARI) for(n=0,50, print1((1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2), ", ")) \\ _G. C. Greubel_, Oct 06 2017
%Y Cf. A047707.
%K easy,nonn
%O 0,4
%A _Vladeta Jovovic_, Goran Kilibarda, Jul 25 2000
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