A165542 Number of permutations of length n which avoid the patterns 4231 and 4123.

1, 1, 2, 6, 22, 89, 380, 1677, 7566, 34676, 160808, 752608, 3548325, 16830544, 80234659, 384132724, 1845829988, 8897740300, 43010084460, 208409687323, 1012046126532, 4923952560917, 23997719075657, 117136530812812, 572552052378494, 2802078324448067

Offset: 0

Author

Vincent Vatter, Sep 21 2009

Keywords

• nonn

Comments

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

Examples

			There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
		

Links

• David Bevan, Jay Pantone, and Nathaniel Shar, Table of n, a(n) for n = 0..1000 (terms 1 through 40 by David Bevan, terms 41 through 70 by Nathaniel Shar)
• Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [math.CO], 2015.
• C. Bean, M. Tannock and H. Ulfarsson, Pattern avoiding permutations and independent sets in graphs, arXiv:1512.08155 [math.CO], 2015.
• 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.
• Wikipedia, Permutation classes avoiding two patterns of length 4.

Crossrefs

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

Extensions

More terms from David Bevan, Feb 04 2014

a(0)=1 prepended by Jay Pantone, Oct 01 2015