A256206 Number of permutations in S_n that avoid the pattern 42315.

1, 1, 2, 6, 24, 119, 694, 4581, 33287, 260967, 2175379, 19072271, 174426353, 1653484169, 16165513608, 162344264849, 1669261805697, 17526017429722, 187472773174466, 2039233971499931, 22520066337196663, 252141732452056894, 2858721279079666465, 32786666580814894741

Offset

0,3

Links

Anthony Guttmann, Table of n, a(n) for n = 0..26

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.

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, 1, 5}], {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.

Cf. A099952.

Sequence in context: A256204 A256205 A116485 * A052397 A047889 A256207

Adjacent sequences: A256203 A256204 A256205 * A256207 A256208 A256209

Keyword

nonn

Author

N. J. A. Sloane, Mar 19 2015

Extensions

More terms from Anthony Guttmann, Sep 29 2021

Status

approved