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A256198 Number of permutations in S_n that avoid the pattern 35124.

%I A256198 #22 Sep 29 2021 02:39:13
%S A256198 1,1,2,6,24,119,694,4580,33249,260092,2159381,18815124,170605392,
%T A256198 1599499163,15427796984,152487271455,1539554179950,15836801521762,
%U A256198 165625811815111,1757953168747511,18908510233855411,205838673911323648,2265393020812413370,25182471016157568626
%N A256198 Number of permutations in S_n that avoid the pattern 35124.
%H A256198 Anthony Guttmann, <a href="/A256198/b256198.txt">Table of n, a(n) for n = 0..27</a>
%H A256198 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 A256198 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 A256198 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256198     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256198     psn = Permutations[Range[n]]},
%t A256198    For[i = 1, i <= Length[lpat], i++,
%t A256198     p = lpat[[i]];
%t A256198     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256198     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256198 Table[avoid[n, {3, 5, 1, 2, 4}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256198 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256198 Cf. A099952.
%K A256198 nonn
%O A256198 0,3
%A A256198 _N. J. A. Sloane_, Mar 19 2015
%E A256198 More terms from _Anthony Guttmann_, Sep 29 2021