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A165542 Number of permutations of length n which avoid the patterns 4231 and 4123.

%I A165542 #41 Nov 09 2016 18:33:10
%S A165542 1,1,2,6,22,89,380,1677,7566,34676,160808,752608,3548325,16830544,
%T A165542 80234659,384132724,1845829988,8897740300,43010084460,208409687323,
%U A165542 1012046126532,4923952560917,23997719075657,117136530812812,572552052378494,2802078324448067
%N A165542 Number of permutations of length n which avoid the patterns 4231 and 4123.
%C A165542 G.f. conjectured to be non-D-finite (see Albert et al link). - _Jay Pantone_, Oct 01 2015
%H A165542 David Bevan, Jay Pantone, and Nathaniel Shar, <a href="/A165542/b165542.txt">Table of n, a(n) for n = 0..1000</a> (terms 1 through 40 by David Bevan, terms 41 through 70 by Nathaniel Shar)
%H A165542 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 A165542 C. Bean, M. Tannock and H. Ulfarsson, <a href="http://arxiv.org/abs/1512.08155">Pattern avoiding permutations and independent sets in graphs</a>, arXiv:1512.08155 [math.CO], 2015.
%H A165542 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 A165542 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 A165542 There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
%Y A165542 Cf. A053614, A106228, A165542, A165545, A257561, A257562.
%K A165542 nonn
%O A165542 0,3
%A A165542 _Vincent Vatter_, Sep 21 2009
%E A165542 More terms from _David Bevan_, Feb 04 2014
%E A165542 a(0)=1 prepended by _Jay Pantone_, Oct 01 2015