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A165538 Number of permutations of length n which avoid the patterns 4312 and 3142. 3
1, 2, 6, 22, 88, 367, 1568, 6810, 29943, 132958, 595227, 2683373, 12170778, 55499358, 254297805, 1170248190, 5406570910, 25068420955, 116617923611, 544157590706, 2546278167018, 11945937322413, 56180864428301 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
M. H. Albert, M. D. Atkinson, and V. Vatter, Inflations of geometric grid classes: three case studies, arXiv:1209.0425 [math.CO], 2012.
Christian Bean, Finding structure in permutation sets, Ph.D. Dissertation, Reykjavík University, School of Computer Science, 2018.
Christian Bean, Émile Nadeau, Henning Ulfarsson, Enumeration of Permutation Classes and Weighted Labelled Independent Sets, arXiv:1912.07503 [math.CO], 2019.
Robert Brignall, Jakub Sliacan, Juxtaposing Catalan permutation classes with monotone ones, arXiv:1611.05370 [math.CO], 2016.
Juan B. Gil, Michael D. Weiner, On pattern-avoiding Fishburn permutations, arXiv:1812.01682 [math.CO], 2018.
Darla Kremer and Wai Chee Shiu, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
FORMULA
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.
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
EXAMPLE
There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
CROSSREFS
Sequence in context: A165536 A032351 A165537 * A165539 A109033 A049135
KEYWORD
nonn
AUTHOR
Vincent Vatter, Sep 21 2009
EXTENSIONS
Reference corrected by Vincent Vatter, Sep 04 2012
STATUS
approved

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Last modified June 26 18:12 EDT 2024. Contains 373720 sequences. (Running on oeis4.)