A256208 Number of permutations in S_n that avoid the pattern 52341.

1, 1, 2, 6, 24, 119, 694, 4582, 33325, 261863, 2192390, 19358590, 178904675, 1720317763, 17132629082, 176055309619, 1861037944163, 20185165186517, 224150069984572, 2543698932578158, 29451619807433107, 347417296695040510, 4170088041714300134, 50874753262007210667

Offset: 0

Author

N. J. A. Sloane, Mar 19 2015

Keywords

• nonn

Links

• Anthony Guttmann, Table of n, a(n) for n = 0..23
• 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.

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

Programs

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, {5, 2, 3, 4, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

Extensions

More terms from Anthony Guttmann, Sep 29 2021