cp's OEIS Frontend

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

%I A256197 #22 Sep 29 2021 02:36:12
%S A256197 1,1,2,6,24,119,694,4579,33218,259483,2149558,18672277,168648090,
%T A256197 1573625606,15093309024,148223240022,1485673163882,15159644212775,
%U A256197 157142812302992,1651865171372967,17582693993265148,189269329080075275,2058215511081891400,22589841589522026553
%N A256197 Number of permutations in S_n that avoid the pattern 35214.
%H A256197 Anthony Guttmann, <a href="/A256197/b256197.txt">Table of n, a(n) for n = 0..26</a>
%H A256197 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 A256197 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 A256197 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256197     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256197     psn = Permutations[Range[n]]},
%t A256197    For[i = 1, i <= Length[lpat], i++,
%t A256197     p = lpat[[i]];
%t A256197     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256197     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256197 Table[avoid[n, {3, 5, 2, 1, 4}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256197 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256197 Cf. A099952.
%K A256197 nonn
%O A256197 0,3
%A A256197 _N. J. A. Sloane_, Mar 19 2015
%E A256197 More terms from _Anthony Guttmann_, Sep 29 2021