A256197 Number of permutations in S_n that avoid the pattern 35214.

1, 1, 2, 6, 24, 119, 694, 4579, 33218, 259483, 2149558, 18672277, 168648090, 1573625606, 15093309024, 148223240022, 1485673163882, 15159644212775, 157142812302992, 1651865171372967, 17582693993265148, 189269329080075275, 2058215511081891400, 22589841589522026553

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, {3, 5, 2, 1, 4}], {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: A224316 A256195 A256196 * A256198 A256199 A256200

Adjacent sequences: A256194 A256195 A256196 * A256198 A256199 A256200

Keyword

nonn

Author

N. J. A. Sloane, Mar 19 2015

Extensions

More terms from Anthony Guttmann, Sep 29 2021

Status

approved