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%I #19 Oct 20 2017 14:36:41
%S 1,2,6,22,86,330,1198,4087,13185,40619,120636,348197,983073,2728722,
%T 7475575,20274288,54558291,145933414,388520823,1030601705,2726043970,
%U 7194657991,18955376065,49872709551,131077883030,344216450494,903332924312,2369406020786
%N Number of permutations of length n which avoid the patterns 2314, 4321.
%H Colin Barker, <a href="/A116708/b116708.txt">Table of n, a(n) for n = 1..1000</a>
%H Darla Kremer and Wai Chee Shiu, <a href="http://dx.doi.org/10.1016/S0012-365X(03)00042-6">Finite transition matrices for permutations avoiding pairs of length four patterns</a>, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Enumerations_of_specific_permutation_classes#Classes_avoiding_two_patterns_of_length_4">Permutation classes avoiding two patterns of length 4</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (13,-74,243,-510,715,-678,429,-173,40,-4).
%F G.f.: -(x*(4*x^9-29*x^8+108*x^7-234*x^6+313*x^5-268*x^4+151*x^3-54*x^2+11*x-1) / ((x-1)^6*(2*x-1)^2*(x^2-3*x+1)).
%o (PARI) Vec((1 - 11*x + 54*x^2 - 151*x^3 + 268*x^4 - 313*x^5 + 234*x^6 - 108*x^7 + 29*x^8 - 4*x^9) / ((1 - x)^6*(1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^30)) \\ _Colin Barker_, Oct 20 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
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