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%I #28 Jul 05 2022 19:40:38
%S 5,19,61,188,523,1387,3565,8888,21674,51928,122522,285434,657789,
%T 1501617,3399771,7641564,17064957,37889229,83688437,183979390,
%U 402729040,878129096,1907861044,4131449572,8919397717,19201879583,41230101641,88313236636,188733236543
%N Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(0,0,3,0)(x).
%C Conjecture: satisfies a linear recurrence having signature (3, 0, 1, -12, -3, 1, 18, 12, 8). - _Harvey P. Dale_, Sep 03 2021
%H S. Kitaev, J. Remmel and M. Tiefenbruck, <a href="http://arxiv.org/abs/1201.6243">Marked mesh patterns in 132-avoiding permutations I</a>, arXiv preprint arXiv:1201.6243, 2012
%F Empirical g.f.: -x^4*(4*x^2+4*x+5) / ((2*x-1)^3*(x^2+x+1)^3). - _Colin Barker_, Jul 22 2013
%t QQQ3[t, x] = 2 /(1+(t*x-t)*(1+t+2*t^2) + ((1 + (t*x - t)*(1 + t + 2*t^2))^2 - 4*t*x)^(1/2)); CoefficientList[Coefficient[Series[QQQ3[t, x], {t, 0, 22}], x], t] (* _Robert Price_, Jun 05 2012 *)
%K nonn
%O 4,1
%A _N. J. A. Sloane_, May 09 2012
%E a(10)-a(22) from _Robert Price_, Jun 04 2012
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