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A256201 Number of permutations in S_n that avoid the pattern 35241.

%I A256201 #21 Sep 29 2021 02:41:18
%S A256201 1,1,2,6,24,119,694,4580,33254,260285,2163930,18900534,172016256,
%T A256201 1621031261,15739870457,156855197297,1599233708733,16638560125635,
%U A256201 176269571712376,1898076560618372,20742488003444465,229747253093647567,2576270755655436479,29218474225923168362
%N A256201 Number of permutations in S_n that avoid the pattern 35241.
%H A256201 Anthony Guttmann, <a href="/A256201/b256201.txt">Table of n, a(n) for n = 0..26</a>
%H A256201 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 A256201 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 A256201 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256201     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256201     psn = Permutations[Range[n]]},
%t A256201    For[i = 1, i <= Length[lpat], i++,
%t A256201     p = lpat[[i]];
%t A256201     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256201     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256201 Table[avoid[n, {3, 5, 2, 4, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256201 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256201 Cf. A099952.
%K A256201 nonn
%O A256201 0,3
%A A256201 _N. J. A. Sloane_, Mar 19 2015
%E A256201 More terms from _Anthony Guttmann_, Sep 29 2021