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%I #40 Oct 23 2023 08:34:32
%S 1,2,6,22,88,367,1568,6810,29943,132958,595227,2683373,12170778,
%T 55499358,254297805,1170248190,5406570910,25068420955,116617923611,
%U 544157590706,2546278167018,11945937322413,56180864428301
%N Number of permutations of length n which avoid the patterns 4312 and 3142.
%H M. H. Albert, M. D. Atkinson, and V. Vatter, <a href="http://arxiv.org/abs/1209.0425">Inflations of geometric grid classes: three case studies</a>, arXiv:1209.0425 [math.CO], 2012.
%H Christian Bean, <a href="https://hdl.handle.net/20.500.11815/1184">Finding structure in permutation sets</a>, Ph.D. Dissertation, Reykjavík University, School of Computer Science, 2018.
%H Christian Bean, Émile Nadeau, Henning Ulfarsson, <a href="https://arxiv.org/abs/1912.07503">Enumeration of Permutation Classes and Weighted Labelled Independent Sets</a>, arXiv:1912.07503 [math.CO], 2019.
%H Robert Brignall, Jakub Sliacan, <a href="https://arxiv.org/abs/1611.05370">Juxtaposing Catalan permutation classes with monotone ones</a>, arXiv:1611.05370 [math.CO], 2016.
%H Juan B. Gil, Michael D. Weiner, <a href="https://arxiv.org/abs/1812.01682">On pattern-avoiding Fishburn permutations</a>, arXiv:1812.01682 [math.CO], 2018.
%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 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>.
%F G.f. f satisfies: (x^3-2*x^2+x)*f^4+(4*x^3-9*x^2+6*x-1)*f^3+(6*x^3-12*x^2+7*x-1)*f^2+(4*x^3-5*x^2+x)*f+x^3 = 0.
%F G.f.: A(x)=B(x)/C(x) where B(x) is the g.f. of A007317 and C(x) is the g.f. of A000108. - _Michael D. Weiner_, Jan 02 2019
%e There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
%K nonn
%O 1,2
%A _Vincent Vatter_, Sep 21 2009
%E Reference corrected by _Vincent Vatter_, Sep 04 2012
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