A165545 Number of permutations of length n which avoid the patterns 2341 and 3421.

1, 1, 2, 6, 22, 89, 382, 1711, 7922, 37663, 182936, 904302, 4535994, 23034564, 118209806, 612165222, 3195359360, 16795435994, 88825567814, 472356139660, 2524292893556, 13549955878141, 73026827854516, 395017112175542, 2143881709415478, 11671226062503926

Offset: 0

Author

Vincent Vatter, Sep 21 2009

Keywords

• nonn

Comments

These permutations have an enumeration scheme of depth 4.

G.f. is 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

• Jay Pantone, Table of n, a(n) for n = 0..1000
• Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [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.
• V. Vatter, Enumeration schemes for restricted permutations, Combin., Prob. and Comput. 17 (2008), 137-159.
• Wikipedia, Permutation classes avoiding two patterns of length 4.

Crossrefs

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

Extensions

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