A256196 - OEIS

%I #25 Sep 29 2021 02:35:31

%S 1,1,2,6,24,119,694,4579,33216,259401,2147525,18632512,167969934,

%T 1563027614,14937175825,146016423713,1455402205257,14753501614541,

%U 151783381341695,1582029822426003,16681492660789425,177726496203056670,1911230701872865231,20726637978574528119

%N Number of permutations in S_n that avoid the pattern 31524.

%H Anthony Guttmann, <a href="/A256196/b256196.txt">Table of n, a(n) for n = 0..25</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, {3, 1, 5, 2, 4}], {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 a(14)-a(16) from _Bert Dobbelaere_, Mar 18 2021

%E More terms from _Anthony Guttmann_, Sep 29 2021