%I #13 Jan 02 2019 23:16:38
%S 0,1,1,5,14,42,112,304,768,1928,4696,11280,26624,62160,143360,327744,
%T 742752,1671296,3735552,8301504,18350080,40370688,88429952,192939008,
%U 419430400,908768000,1962934272,4227862528,9082066432,19461578752,41607495680,88762674176,188978561024,401579474944
%N Number of symmetry classes of 3-eared triangulations of an n-gon.
%H A. Regev, <a href="http://arxiv.org/abs/1309.0743">Remarks on two-eared triangulations</a>, arXiv preprint arXiv:1309.0743 [math.CO], 2013-2014.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,-2,12,4,8,-48,32).
%F See Maple code.
%F G.f.: -x^6*(1-5*x+9*x^2-4*x^3-2*x^4+8*x^6-6*x^5) / ( (2*x^2-1)*(2*x^3-1)*(2*x-1)^3 ). - _R. J. Mathar_, Dec 04 2013
%p f:=proc(n) local t1;
%p t1:=2^(n-8)*(n-4)*(n-5)/3;
%p if (n mod 2) = 0 then t1:=t1+2^(n/2-4); fi;
%p if (n mod 3) = 0 then t1:=t1+2^(n/3-2)/3; fi;
%p t1; end;[seq(f(n),n=5..50)];
%t LinearRecurrence[{6, -10, -2, 12, 4, 8, -48, 32}, {0, 1, 1, 5, 14, 42, 112, 304}, 40] (* _Jean-François Alcover_, Dec 06 2017 *)
%Y Cf. A005418.
%K nonn
%O 5,4
%A _N. J. A. Sloane_, Dec 02 2013
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