%I #10 Mar 21 2021 21:38:54
%S 1,1,2,6,21,76,270,927,3074,9886,30985,95064,286558,851203,2497550,
%T 7252494,20874861,59630404,169225518,477513639,1340705306,3747697726,
%U 10435070737,28954040496,80087091646,220897122571,607726482470,1668084221742,4568859998709,12489795988636
%N Number of permutations of [n] avoiding {1324, 2431, 3241}.
%H Colin Barker, <a href="/A294817/b294817.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 1 No 184.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-31,51,-41,15,-2).
%F From _Colin Barker_, Nov 23 2017: (Start)
%F a(n) = (1/25)*(2^(-1-n)*(-25*2^(1+n) + 75*2^(1+2*n) - 25*(3+sqrt(5))^n - 37*sqrt(5)*(3+sqrt(5))^n + (3-sqrt(5))^n*(-25+37*sqrt(5)) + 20*((3-sqrt(5))^n + (3+sqrt(5))^n)*n)).
%F a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 41*a(n-4) + 15*a(n-5) - 2*a(n-6) for n>5.
%F (End)
%p (1 -8*x +24*x^2 -32*x^3 +19*x^4 -3*x^5)/((1 -x)*(1 -2*x)*(1 -3*x +x^2)^2) ;
%p taylor(%,x=0,40) ;
%p gfun[seriestolist](%) ;
%o (PARI) Vec((1 -8*x +24*x^2 -32*x^3 +19*x^4 -3*x^5)/((1 -x)*(1 -2*x)*(1 -3*x +x^2)^2) + O(x^40)) \\ _Colin Barker_, Nov 23 2017
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Nov 09 2017