%I #34 May 17 2018 16:49:01
%S 1,1,2,5,14,28,62,143,331,738,1665,3780,8576,19376,43837,99265,224734,
%T 508553,1151002,2605348,5897126,13347243,30210075,68378310,154768501,
%U 350303176,792878672,1794610400,4061937929,9193821553,20809373642,47100123053,106606829446,241294807548
%N G.f.: 1/(1-x-x^2-2*x^3-5*x^4).
%C Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,0,4,0)(x).
%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 [math.CO], 2012.
%H Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck, <a href="http://www.emis.de/journals/INTEGERS/papers/p16/p16.Abstract.html">Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II</a>, Electronic Journal of Combinatorial Number Theory, Volume 15 #A16. (<a href="http://arxiv.org/abs/1302.2274">arXiv:1302.2274</a>)
%H Anthony Zaleski, Doron Zeilberger, <a href="https://arxiv.org/abs/1712.10072">On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts</a>, arXiv:1712.10072 [math.CO], 2017.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,2,5).
%t QQQ4[t, x] = 2/(1 +(t*x-t) *(1+t+2*t^2+5*t^3) + ((1+(t*x-t) *(1+t+2*t^2+5*t^3))^2 -4*t*x)^(1/2)); q = Simplify[Series[QQQ4[t, x], {t, 0, 22}]]; CoefficientList[q /. x -> 0, t] (* _Robert Price_, Jun 04 2012 *)
%t LinearRecurrence[{1, 1, 2, 5}, {1, 1, 2, 5}, 34] (* _Jean-François Alcover_, Sep 21 2017 *)
%o (PARI) Vec(1/(1-x-x^2-2*x^3-5*x^4) + O(x^100)) \\ _Altug Alkan_, Nov 01 2015
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 09 2012
%E a(10)-a(22) from _Robert Price_, Jun 04 2012
%E Edited by _N. J. A. Sloane_, Feb 17 2018