A256196 Number of permutations in S_n that avoid the pattern 31524.

1, 1, 2, 6, 24, 119, 694, 4579, 33216, 259401, 2147525, 18632512, 167969934, 1563027614, 14937175825, 146016423713, 1455402205257, 14753501614541, 151783381341695, 1582029822426003, 16681492660789425, 177726496203056670, 1911230701872865231, 20726637978574528119

Offset

0,3

Links

Anthony Guttmann, Table of n, a(n) for n = 0..25

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, 1, 5, 2, 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: A264781 A224316 A256195 * A256197 A256198 A256199

Adjacent sequences: A256193 A256194 A256195 * A256197 A256198 A256199

Keyword

nonn

Author

N. J. A. Sloane, Mar 19 2015

Extensions

a(14)-a(16) from Bert Dobbelaere, Mar 18 2021

More terms from Anthony Guttmann, Sep 29 2021

Status

approved