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%I #19 Feb 03 2024 11:00:31
%S 0,0,0,1,5,18,53,135,305,633,1220,2217,3834,6359,10172,15776,23807,
%T 35075,50585,71576,99551,136332,184084,245384,323260,421256,543484,
%U 694709,880393,1106798,1381049,1711231,2106469,2577049,3134488,3791677,4562974,5464339,6513448
%N Number of 3-element proper antichains (i.e., antichains such that every two members have nonempty intersection) on an unlabeled n-element set.
%H Andrew Howroyd, <a href="/A056782/b056782.txt">Table of n, a(n) for n = 0..1000</a>
%H Vladeta Jovovic, <a href="/A056782/a056782.pdf">Illustration of initial terms</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*(1 + x + 2*x^2 + 3*x^3 + 3*x^4 - x^5 - 3*x^7)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2). - _Andrew Howroyd_, Feb 02 2024
%o (PARI) seq(n)=Vec((1 + x + 2*x^2 + 3*x^3 + 3*x^4 - x^5 - 3*x^7)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2) + O(x^(n-2)), -(n+1)) \\ _Andrew Howroyd_, Feb 02 2024
%Y Cf. A001206, A047707, A051303 (labeled case), A055484, A055485, A056005.
%K nonn,easy
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Aug 18 2000
%E a(8) onwards from _Andrew Howroyd_, Feb 02 2024
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