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A256200 Number of permutations in S_n that avoid the pattern 42351.

%I A256200 #25 Sep 29 2021 02:39:55
%S A256200 1,1,2,6,24,119,694,4580,33252,260204,2161930,18861307,171341565,
%T A256200 1610345257,15579644765,154541844196,1566713947713,16190122718865,
%U A256200 170171678529883,1816001425551270,19646035298044543,215179180467834605,2383465957654163227,26673704385975326866
%N A256200 Number of permutations in S_n that avoid the pattern 42351.
%H A256200 Anthony Guttmann, <a href="/A256200/b256200.txt">Table of n, a(n) for n = 0..27</a>
%H A256200 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 A256200 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.
%F A256200 a(n) = n! - A158434(n). - _Andrew Howroyd_, May 18 2020
%t A256200 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256200     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256200     psn = Permutations[Range[n]]},
%t A256200    For[i = 1, i <= Length[lpat], i++,
%t A256200     p = lpat[[i]];
%t A256200     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256200     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256200 Table[avoid[n, {4, 2, 3, 5, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256200 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256200 Cf. A099952, A158434.
%K A256200 nonn
%O A256200 0,3
%A A256200 _N. J. A. Sloane_, Mar 19 2015
%E A256200 a(14)-a(15) added by _Andrew Howroyd_, May 18 2020
%E A256200 More terms from _Anthony Guttmann_, Sep 29 2021