%I #13 Mar 21 2021 21:04:53
%S 1,1,2,6,21,73,238,722,2054,5541,14323,35788,87043,207201,484772,
%T 1118334,2550164,5759101,12899521,28689880,63419177,139435017,
%U 305102778,664755562,1442788402,3120497429,6727583999,14461863108,31004177695,66303416497,141465316864,301184381814,639949891424
%N Number of permutations of [n] avoiding {1243, 2314, 3412}.
%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1708.00832">Enumeration of small Wilf Classes avoiding 1342 and two other 4-letter patterns</a>, arXiv:1708.00832 (2017). Table 1 No 77.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12,-63,190,-363,456,-377,198,-60,8).
%F O.g.f.: (1 - 11*x + 53*x^2 - 145*x^3 + 248*x^4 - 274*x^5 + 192*x^6 - 80*x^7 + 17*x^8)/((1 - 2*x)^3*(1 - x)^6).
%F a(n) = -n^5/120 + n^4/24 - n^3/24 + (3*2^n + 35)*n^2/24 + (35*2^n + 142)*n/40 - (7*2^n - 8). - _Bruno Berselli_, Nov 07 2017
%p p := 1-11*x+53*x^2-145*x^3+248*x^4-274*x^5+192*x^6-80*x^7+17*x^8 ;
%p q := (1-x)^6*(1-2*x)^3 ;
%p taylor(p/q,x=0,40) ;
%p gfun[seriestolist](%) ;
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Nov 07 2017