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

Author

Jay Pantone, Apr 30 2015

Keywords

• nonn

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

Examples

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

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).

Crossrefs

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