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A256200 Number of permutations in S_n that avoid the pattern 42351. 2
1, 1, 2, 6, 24, 119, 694, 4580, 33252, 260204, 2161930, 18861307, 171341565, 1610345257, 15579644765, 154541844196, 1566713947713, 16190122718865, 170171678529883, 1816001425551270, 19646035298044543, 215179180467834605, 2383465957654163227, 26673704385975326866 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.
FORMULA
a(n) = n! - A158434(n). - Andrew Howroyd, May 18 2020
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, {4, 2, 3, 5, 1}], {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.
Sequence in context: A256197 A256198 A256199 * A256201 A256202 A256203
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 19 2015
EXTENSIONS
a(14)-a(15) added by Andrew Howroyd, May 18 2020
More terms from Anthony Guttmann, Sep 29 2021
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)