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%I #18 Mar 21 2021 21:47:49
%S 1,1,2,6,21,73,240,748,2240,6525,18653,52640,147210,408957,1130398,
%T 3112172,8540753,23375439,63830072,173949534,473211976,1285299971,
%U 3486071977,9442928926,25548319586,69046732343,186416183910,502821645418,1355067144205,3648781579445,9817397466928
%N Number of permutations of [n] avoiding {1243, 2431, 3412}.
%H Colin Barker, <a href="/A294695/b294695.txt">Table of n, a(n) for n = 0..1000</a>
%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 90.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12,-61,172,-296,322,-221,92,-21,2).
%F O.g.f.: (1 - 11*x + 51*x^2 - 129*x^3 + 195*x^4 - 183*x^5 + 104*x^6 - 30*x^7 + 3*x^8) / ((1 - x)^4*(1 - 2*x)*(1 - 3*x + x^2)^2).
%F a(n) = 12*a(n-1) - 61*a(n-2) + 172*a(n-3) - 296*a(n-4) + 322*a(n-5) - 221*a(n-6) + 92*a(n-7) - 21*a(n-8) + 2*a(n-9) for n>8. - _Colin Barker_, Nov 07 2017
%p p := 1-11*x+51*x^2-129*x^3+195*x^4-183*x^5+104*x^6-30*x^7+3*x^8 ;
%p q := (1-x)^4*(1-2*x)*(1-3*x+x^2)^2 ;
%p taylor(p/q,x=0,40) ;
%p gfun[seriestolist](%) ;
%o (PARI) Vec((1 - 11*x + 51*x^2 - 129*x^3 + 195*x^4 - 183*x^5 + 104*x^6 - 30*x^7 + 3*x^8) / ((1 - x)^4*(1 - 2*x)*(1 - 3*x + x^2)^2) + O(x^30)) \\ _Colin Barker_, Nov 07 2017
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Nov 07 2017
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