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A257562 Number of permutations of length n that avoid the patterns 4123, 4231, and 4312. 4
1, 1, 2, 6, 21, 79, 310, 1251, 5150, 21517, 90921, 387595, 1663936, 7183750, 31158310, 135661904, 592558096, 2595232344, 11392504426, 50109205789, 220777103354, 974162444028, 4303957562319, 19036842605855, 84285643628790, 373502845338552, 1656428550764640, 7351106011540209, 32643855249507805, 145040974005303590, 644756480385363800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

G.f. conjectured to be non-D-finite (see Albert et al. link). Jay Pantone, Oct 01 2015

Unlike A061552, whose g.f. is also conjectured to be non-D-finite, thousands of terms of the counting sequence are known. - David Callan, Aug 29 2017

LINKS

Jay Pantone, Table of n, a(n) for n = 0..5000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017).

David Callan, Toufik Mansour, Mark Shattuck, Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done, Pure Mathematics and Applications (2019) Vol. 28, Issue 1, 14-69.

Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [math.CO], (2015).

EXAMPLE

a(4) = 21 because there are 24 permutations of length 4 and 3 of them do not avoid 4123, 4231, and 4312.

CROSSREFS

Cf. A053614, A106228, A165542, A165545, A257561, A257562.

Sequence in context: A111279 A150197 A150198 * A033321 A050203 A112806

Adjacent sequences:  A257559 A257560 A257561 * A257563 A257564 A257565

KEYWORD

nonn

AUTHOR

Jay Pantone, Apr 30 2015

STATUS

approved

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Last modified June 18 10:54 EDT 2021. Contains 345098 sequences. (Running on oeis4.)