

A257561


Number of permutations of length n that avoid the patterns 4231, 4312, and 4321.


5



1, 1, 2, 6, 21, 80, 322, 1346, 5783, 25372, 113174, 511649, 2338988, 10793251, 50205607, 235156609, 1108120540, 5249646137, 24987770893, 119443412277, 573125649031, 2759515312908, 13328311926552, 64559295743113, 313530998739472, 1526333617345412, 7447070497787110, 36409703715788374, 178353171835771153, 875224495042876048, 4302111437028045585
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OFFSET

0,3


COMMENTS

a(n) is the number of permutations of length n avoiding the partially ordered pattern (POP) {1>2, 1>3, 2>4} of length 4. That is, the number of length n permutations having no subsequences of length 4 in which the first element is the largest and the second element is larger than the fourth element.  Sergey Kitaev, Dec 09 2020


LINKS

Jay Pantone, Table of n, a(n) for n = 0..500
Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [math.CO], 2015.
D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 1 No. 241.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.


FORMULA

G.f. satisfies (2*x^2+8*x1)*F(x)^4 + (x^3+4*x^246*x+5)*F(x)^3 + (3*x^321*x^2+94*x9)*F(x)^2 + (x^3+12*x^282*x+7)*F(x) + 3*x^2+26*x2 = 0.  Jay Pantone, Oct 01 2015


EXAMPLE

a(4) = 21 because there are 24 permutations of length 4, and 3 of them do not avoid 4231, 4312, and 4321.


CROSSREFS

Sequence in context: A150202 A106223 A196345 * A150203 A106228 A150204
Adjacent sequences: A257558 A257559 A257560 * A257562 A257563 A257564


KEYWORD

nonn


AUTHOR

Jay Pantone, Apr 30 2015


STATUS

approved



