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%I #12 Mar 22 2021 02:52:17
%S 1,1,2,6,21,75,259,852,2669,7997,23043,64190,173677,458255,1183139,
%T 2997544,7470237,18349057,44497747,106691218,253229501,595589331,
%U 1389361107,3217028796,7398749581,16911430725,38436598499,86905975142,195555225549,438086659607,977373490243,2172179704400,4810363365437
%N Number of permutations of [n] avoiding {1324, 3421, 3241}.
%H Colin Barker, <a href="/A294806/b294806.txt">Table of n, a(n) for n = 0..1000</a>
%H D. Callan and 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 1 No 150.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (12,-62,180,-321,360,-248,96,-16).
%F G.f.: (1 - 11*x + 52*x^2 - 136*x^3 + 214*x^4 - 204*x^5 + 111*x^6 - 28*x^7) / ((1 - x)^4*(1 - 2*x)^4).
%F From _Colin Barker_, Nov 10 2017: (Start)
%F a(n) = (1/24)*(24*(2^(2 + n)-3) + 5*(2^n-16)*n - 6*(2^n+2)*n^2 + (2^n-4)*n^3).
%F a(n) = 12*a(n-1) - 62*a(n-2) + 180*a(n-3) - 321*a(n-4) + 360*a(n-5) - 248*a(n-6) + 96*a(n-7) - 16*a(n-8) for n>7.
%F (End)
%p (1 -11*x +52*x^2 -136*x^3 +214*x^4 -204*x^5 +111*x^6 -28*x^7)/((1 -x)^3*(1 -2*x)^3*(1 -3*x +2*x^2)) ;
%p taylor(%,x=0,40) ;
%p gfun[seriestolist](%) ;
%o (PARI) Vec((1 - 11*x + 52*x^2 - 136*x^3 + 214*x^4 - 204*x^5 + 111*x^6 - 28*x^7) / ((1 - x)^4*(1 - 2*x)^4) + O(x^30)) \\ _Colin Barker_, Nov 10 2017
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Nov 09 2017
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