A116485 - OEIS

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A116485

Number of permutations in S_n that avoid the pattern 12453 (or equivalently, 31245).

1, 1, 2, 6, 24, 119, 694, 4581, 33286, 260927, 2174398, 19053058, 174094868, 1648198050, 16085475576, 161174636600, 1652590573612, 17292601075489, 184246699159418, 1995064785620557, 21919480341617102, 244015986016996763, 2749174129340156922, 31313478171012371344 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`a(n) is also the number of permutations in S_n that avoid the pattern 21453 or any of its symmetries. The Wilf class consists of 16 permutations. - David Bevan, Jun 17 2021`
	LINKS	`Yonah Biers-Ariel, Table of n, a(n) for n = 0..37` `Yonah Biers-Ariel, Julia program to compute terms` `Miklos Bona, The limit of a Stanley-Wilf sequence is not always rational, and layered patterns beat monotone patterns, arXiv:math/0403502 [math.CO], 2004.` `Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.`
	FORMULA	`Conjecture: a(n) + A158423(n) = n!. - Benedict W. J. Irwin, Mar 15 2016` `The conjecture is true: All that is needed is to show that 23145 is Wilf-equivalent to 31245, but that’s obvious since they are inverses. - Doron Zeilberger and Yonah Biers-Ariel, Feb 26 2019` `The exponential growth rate is 9+4*sqrt(2). See [Bona 2004]. - David Bevan, Jun 17 2021`
	MATHEMATICA	`avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,` `lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],` `psn = Permutations[Range[n]]},` `For[i = 1, i <= Length[lpat], i++,` `p = lpat[[i]];` `AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];` `]; n! - Length[Union[Flatten[lseq, 1]]]];` `Table[avoid[n, {1, 2, 4, 5, 3}], {n, 0, 8}] (* Robert Price, Mar 27 2020 *)`
	CROSSREFS	`Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208. - N. J. A. Sloane, Mar 19 2015` `Cf. A099952, A158423.` `Sequence in context: A256203 A256204 A256205 * A256206 A052397 A047889` `Adjacent sequences: A116482 A116483 A116484 * A116486 A116487 A116488`
	KEYWORD	`nonn`
	AUTHOR	`Zvezdelina Stankova (stankova(AT)mills.edu), Mar 19 2006`
	EXTENSIONS	`More terms from the Zvezdelina Stankova-Frenkel and Julian West paper. - N. J. A. Sloane, Mar 19 2015` `More terms from Doron Zeilberger and Yonah Biers-Ariel, Feb 26 2019` `More terms from Yonah Biers-Ariel, Mar 04 2019`
	STATUS	`approved`

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Last modified March 25 01:20 EDT 2023. Contains 361511 sequences. (Running on oeis4.)