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A256202 Number of permutations in S_n that avoid the pattern 53241.

%I A256202 #21 Sep 29 2021 02:42:06
%S A256202 1,1,2,6,24,119,694,4580,33256,260370,2166120,18945144,172810050,
%T A256202 1633997788,15939893003,159820729208,1641980432159,17242378256155,
%U A256202 184674461615836,2013829450204384,22324460502429244,251250502143635615,2867467023751687892,33152272498223444540
%N A256202 Number of permutations in S_n that avoid the pattern 53241.
%H A256202 Anthony Guttmann, <a href="/A256202/b256202.txt">Table of n, a(n) for n = 0..26</a>
%H A256202 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 A256202 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 A256202 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256202     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256202     psn = Permutations[Range[n]]},
%t A256202    For[i = 1, i <= Length[lpat], i++,
%t A256202     p = lpat[[i]];
%t A256202     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256202     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256202 Table[avoid[n, {5, 3, 2, 4, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256202 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256202 Cf. A099952.
%K A256202 nonn
%O A256202 0,3
%A A256202 _N. J. A. Sloane_, Mar 19 2015
%E A256202 More terms from _Anthony Guttmann_, Sep 29 2021