A257562 Number of permutations of length n that avoid the patterns 4123, 4231, and 4312.

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

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