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A263790 The number of length-n permutations avoiding the patterns 1234, 1324 and 2143.

%I A263790 #49 Sep 08 2022 08:46:14
%S A263790 1,1,2,6,21,75,268,958,3425,12245,43778,156514,559565,2000543,7152292,
%T A263790 25570698,91419729,326841561,1168515890,4177649198,14935828405,
%U A263790 53398205443,190907947468,682529386598,2440162233937,8724007852045,31189857766034,111509210441322,398664979703373
%N A263790 The number of length-n permutations avoiding the patterns 1234, 1324 and 2143.
%H A263790 C. Bean, M. Tannock and H. Ulfarsson, <a href="http://arxiv.org/abs/1512.08155">Pattern avoiding permutations and independent sets in graphs</a>, arXiv:1512.08155 [math.CO], 2015, eq. (4).
%H A263790 D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 [math.CO] (2017), Table 2 No 181.
%H A263790 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,2,-1).
%F A263790 G.f.: (2*x^3 + 3*x - 1)/(-x^4 + 2*x^3 - 2*x^2 + 4*x - 1).
%p A263790 t1:=(1-3*x-2*x^3)/(1-4*x+2*x^2-2*x^3+x^4);
%p A263790 series(t1,x,40);
%p A263790 seriestolist(%); # _N. J. A. Sloane_, Nov 09 2016
%t A263790 LinearRecurrence[{4, -2, 2, -1}, {1, 1, 2, 6}, 30] (* _Jean-François Alcover_, Dec 31 2015 *)
%t A263790 CoefficientList[Series[(2 x^3 + 3 x - 1)/(-x^4 + 2*x^3 - 2 x^2 + 4 x - 1), {x, 0, 35}], x] (* _Vincenzo Librandi_, Jan 01 2016 *)
%o A263790 (PARI) Vec((2*x^3 + 3*x - 1)/(-x^4 + 2*x^3 - 2*x^2 + 4*x - 1) + O(x^50)) \\ _Michel Marcus_, Nov 23 2015
%o A263790 (Magma) I:=[1,1,2,6]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jan 01 2016
%K A263790 nonn,easy
%O A263790 0,3
%A A263790 _Christian Bean_, Nov 23 2015