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A165545 Number of permutations of length n which avoid the patterns 2341 and 3421.

%I A165545 #15 Oct 02 2015 05:44:46
%S A165545 1,1,2,6,22,89,382,1711,7922,37663,182936,904302,4535994,23034564,
%T A165545 118209806,612165222,3195359360,16795435994,88825567814,472356139660,
%U A165545 2524292893556,13549955878141,73026827854516,395017112175542,2143881709415478,11671226062503926
%N A165545 Number of permutations of length n which avoid the patterns 2341 and 3421.
%C A165545 These permutations have an enumeration scheme of depth 4.
%C A165545 G.f. is conjectured to be non-D-finite (see Albert et al link). - _Jay Pantone_, Oct 01 2015
%H A165545 Jay Pantone, <a href="/A165545/b165545.txt">Table of n, a(n) for n = 0..1000</a>
%H A165545 Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, <a href="http://arxiv.org/abs/1510.00269">Generating Permutations with Restricted Containers</a>, arXiv:1510.00269 [math.CO], 2015.
%H A165545 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 A165545 V. Vatter, <a href="http://www.math.ufl.edu/~vatter/publications/wilfplus/">Enumeration schemes for restricted permutations</a>, Combin., Prob. and Comput. 17 (2008), 137-159.
%H A165545 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>.
%e A165545 There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
%Y A165545 Cf. A053614, A106228, A165542, A165545, A257561, A257562.
%K A165545 nonn
%O A165545 0,3
%A A165545 _Vincent Vatter_, Sep 21 2009
%E A165545 a(0)=1 prepended by _Jay Pantone_, Oct 01 2015