A256208 - OEIS

%I #21 Sep 29 2021 02:43:28

%S 1,1,2,6,24,119,694,4582,33325,261863,2192390,19358590,178904675,

%T 1720317763,17132629082,176055309619,1861037944163,20185165186517,

%U 224150069984572,2543698932578158,29451619807433107,347417296695040510,4170088041714300134,50874753262007210667

%N Number of permutations in S_n that avoid the pattern 52341.

%H Anthony Guttmann, <a href="/A256208/b256208.txt">Table of n, a(n) for n = 0..23</a>

%H Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, <a href="https://arxiv.org/abs/2109.13485">Classical length-5 pattern-avoiding permutations</a>, arXiv:2109.13485 [math.CO], 2021.

%H Zvezdelina Stankova-Frenkel and Julian West, <a href="http://arxiv.org/abs/math/0103152">A new class of Wilf-equivalent permutations</a>, arXiv:math/0103152 [math.CO], 2001.

%t avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,

%t     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],

%t     psn = Permutations[Range[n]]},

%t    For[i = 1, i <= Length[lpat], i++,

%t     p = lpat[[i]];

%t     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];

%t     ]; n! - Length[Union[Flatten[lseq, 1]]]];

%t Table[avoid[n, {5, 2, 3, 4, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)

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

%Y Cf. A099952.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Mar 19 2015

%E More terms from _Anthony Guttmann_, Sep 29 2021