%I #14 Feb 03 2024 11:01:32
%S 0,0,0,2,9,30,84,202,437,872,1627,2874,4853,7882,12383,18902,28130,
%T 40934,58391,81812,112790,153238,205430,272054,356270,461754,592774,
%U 754252,951831,1191956,1481962,1830144,2245867,2739658,3323305,4009972,4814323,5752624,6842893
%N Number of 3-element antichains on an unlabeled n-element set; equivalence classes of monotone Boolean functions of n variables with 3 mincuts under action of symmetric group S_n.
%D V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H Andrew Howroyd, <a href="/A056778/b056778.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>.
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,2,4,3,-12,3,4,2,-2,-4,4,-1).
%F G.f.: x^3*(2 + x + 2*x^2 + 4*x^3 - x^5 - 2*x^6)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2). - _Andrew Howroyd_, Feb 02 2024
%e There are 30 3-element antichains on an unlabeled 5-element set: {{5},{4},{3}}, {{5},{4},{2,3}}, {{5},{4},{1,2,3}}, {{5},{3,4},{2,4}}, {{5},{3,4},{1,2}}, {{5},{3,4},{1,2,4}}, {{5},{2,3,4},{1,3,4}}, {{4,5},{3,5},{3,4}}, {{4,5},{3,5},{2,5}}, {{4,5},{3,5},{2,4}},{{4,5},{3,5},{2,3,4}}, {{4,5},{3,5},{1,2}}, {{4,5},{3,5},{1,2,5}}, {{4,5},{3,5},{1,2,4}}, {{4,5},{3,5},{1,2,3,4}}, {{4,5},{2,3},{1,3,5}}, {{4,5},{2,3,5},{2,3,4}}, {{4,5},{2,3,5},{1,3,5}}, {{4,5},{2,3,5},{1,3,4}}, {{4,5},{2,3,5},{1,2,3}}, {{4,5},{2,3,5},{1,2,3,4}}, {{4,5},{1,2,3,5},{1,2,3,4}}, {{3,4,5},{2,4,5},{2,3,5}}, {{3,4,5},{2,4,5},{1,4,5}}, {{3,4,5},{2,4,5},{1,3,5}}, {{3,4,5},{2,4,5},{1,2,3}}, {{3,4,5},{2,4,5},{1,2,3,5}}, {{3,4,5},{1,2,5},{1,2,3,4}}, {{3,4,5},{1,2,4,5},{1,2,3,5}}, {{2,3,4,5},{1,3,4,5},{1,2,4,5}}.
%o (PARI) seq(n)=Vec((2 + x + 2*x^2 + 4*x^3 - x^5 - 2*x^6)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2) + O(x^(n-2)), -(n+1)) \\ _Andrew Howroyd_, Feb 02 2024
%Y Cf. A056005, A047707, A055484, A055485.
%K nonn,easy
%O 0,4
%A _Vladeta Jovovic_, Goran Kilibarda, Aug 17 2000
%E a(8) onwards from _Andrew Howroyd_, Feb 02 2024