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%I #16 Oct 20 2017 14:36:26
%S 1,2,6,22,86,330,1206,4174,13726,43134,130302,380414,1078270,2978814,
%T 8046590,21311486,55468030,142147582,359268350,896794622,2213543934,
%U 5408292862,13091995646,31424774142,74845257726,176991240190,415789744126,970830381054
%N Number of permutations of length n which avoid the patterns 2134, 3421.
%H Colin Barker, <a href="/A116706/b116706.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-50,120,-160,112,-32).
%F G.f.: x*(1 - 9*x + 34*x^2 - 64*x^3 + 64*x^4 - 28*x^5 + 4*x^6) / ((1 - x)*(1 - 2*x)^5)
%F From _Colin Barker_, Oct 20 2017: (Start)
%F a(n) = (24*(-32+39*2^n) - 263*2^(1+n)*n + 165*2^n*n^2 - 13*2^(1+n)*n^3 + 3*2^n*n^4) / 384 for n>1.
%F a(n) = 11*a(n-1) - 50*a(n-2) + 120*a(n-3) - 160*a(n-4) + 112*a(n-5) - 32*a(n-6) for n>7.
%F (End)
%o (PARI) Vec(x*(1 - 9*x + 34*x^2 - 64*x^3 + 64*x^4 - 28*x^5 + 4*x^6) / ((1 - x)*(1 - 2*x)^5) + O(x^30)) \\ _Colin Barker_, Oct 20 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006