%I #15 Oct 20 2017 14:36:48
%S 1,2,6,22,86,336,1290,4870,18164,67234,247786,911120,3346618,12286942,
%T 45104548,165573482,607817410,2231360192,8191763970,30074097062,
%U 110410946820,405353571346,1488185247962,5463619641904,20058759689642,73642362774478,270365534734372
%N Number of permutations of length n which avoid the patterns 2341, 4213.
%H Colin Barker, <a href="/A116709/b116709.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,25,-10,2).
%F G.f.: -x*(2*x^4-7*x^3+12*x^2-6*x+1) / (2*x^5-10*x^4+25*x^3-22*x^2+8*x-1).
%F a(n) = 8*a(n-1) - 22*a(n-2) + 25*a(n-3) - 10*a(n-4) + 2*a(n-5) for n>5. - _Colin Barker_, Oct 20 2017
%o (PARI) Vec(x*(1 - 6*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - 8*x + 22*x^2 - 25*x^3 + 10*x^4 - 2*x^5) + O(x^30)) \\ _Colin Barker_, Oct 20 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006