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 A053617 Number of permutations of length n which avoid the patterns 1234 and 1324. 3
 1, 1, 2, 6, 22, 90, 396, 1837, 8864, 44074, 224352, 1163724, 6129840, 32703074, 176351644, 959658200, 5262988330, 29057961666, 161374413196, 900792925199, 5050924332096, 28434661250454, 160644331001476, 910455895039056, 5174722258676440, 29486753617569684 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS These permutations have an "enumeration scheme" of depth 4, see D. Zeilberger's article in the links. G.f. conjectured to be non-D-finite (see Albert et al. link). - Jay Pantone, Oct 01 2015 a(n) is the number of permutations of length n avoiding the partially ordered pattern (POP) {1>2, 1>3, 2>4, 3>4} of length 4. That is, the number of length n permutations having no subsequences of length 4 in which the first element is the largest and the fourth element is the smallest. - Sergey Kitaev, Dec 10 2020 LINKS Andrew Baxter and Jay Pantone, Table of n, a(n) for n = 0..600 (terms n=1..100 from Andrew Baxter) Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [math.CO], 2015. Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019. Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26. Kremer, Darla and Shiu, Wai Chee, 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. D. Zeilberger, Enumeration schemes and more importantly their automatic generation, Annals of Combinatorics 2 (1998) 185-195. The link is to an overview on Doron Zeilberger's home page; there is a local copy here [Pdf file only, no active links] CROSSREFS Cf. A032351, A053614, A106228, A165542, A165545, A257561, A257562. Sequence in context: A340892 A165546 A279568 * A089449 A264601 A374551 Adjacent sequences: A053614 A053615 A053616 * A053618 A053619 A053620 KEYWORD nonn AUTHOR Moa Apagodu, Mar 20 2000 EXTENSIONS More terms from Andrew Baxter, May 20 2011 STATUS approved

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Last modified September 9 14:16 EDT 2024. Contains 375764 sequences. (Running on oeis4.)