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%I #45 Mar 07 2020 01:28:54
%S 0,0,0,2,64,1090,14000,153762,1533504,14356610,128722000,1119607522,
%T 9528462944,79817940930,660876543600,5424917141282,44246078560384,
%U 359144709794050,2904688464582800,23429048035827042,188593339362097824
%N Number of monotone Boolean functions of n variables with 3 mincuts. Also Sperner systems with 3 blocks.
%C The paper by G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), mentions many sequences, but since only very condensed formulas are given, it is hard to match them with entries in the OEIS. It would be nice to add this reference to all the sequences that it mentions. - _N. J. A. Sloane_, Jan 01 2016
%C Term a(1108) has 1000 decimal digits. - _Michael De Vlieger_, Jan 26 2016
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 292, #8, s(n,3).
%H Michael De Vlieger, <a href="/A047707/b047707.txt">Table of n, a(n) for n = 0..1107</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath030.htm">Dedekind's problem.</a>
%H Vladeta Jovovic, <a href="/A047707/a047707.pdf">Illustration for A016269, A047707, A051112-A051118</a>
%H G. Kilibarda, <a href="http://dx.doi.org/10.2298/PIM140406001K">Enumeration of certain classes of antichains</a>, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), 69-87 DOI: 10.2298/PIM140406001K. See page 86, formula for alpha^hat(3,n).
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.html">Antichains of Multisets</a>, J. Integer Seqs., Vol. 7, 2004.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (28,-315,1820,-5684,9072,-5760).
%F a(n) = (2^n)*(2^n - 1)*(2^n - 2)/6 - (6^n - 5^n - 4^n + 3^n).
%F G.f.: -2*x^3*(36*x^2-4*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - _Colin Barker_, Jul 31 2012
%F a(n) = Binomial(2^n,3) - (6^n - 5^n - 4^n + 3^n). - _Ross La Haye_, Jan 26 2016
%t Table[Binomial[2^n, 3] - (6^n - 5^n - 4^n + 3^n), {n, 20}] (* or *)
%t CoefficientList[Series[-2 x^3 (36 x^2 - 4 x - 1)/((2 x - 1) (3 x - 1) (4 x - 1) (5 x - 1) (6 x - 1) (8 x - 1)), {x, 0, 20}], x] (* _Michael De Vlieger_, Jan 26 2016 *)
%o (PARI) a(n)=binomial(2^n,3)-(6^n-5^n-4^n+3^n) \\ _Charles R Greathouse IV_, Apr 08 2016
%Y Cf. A016269, A051112.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
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