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A256205 Number of permutations in S_n that avoid the pattern 34215.

%I A256205 #21 Sep 29 2021 02:37:29
%S A256205 1,1,2,6,24,119,694,4581,33285,260886,2173374,19032746,173741467,
%T A256205 1642533692,15999488304,159917206735,1634681988983,17042352950764,
%U A256205 180798150762914,1948027746498015,21282786390947602,235446451502773103,2634317655935012208,29778833170013213300
%N A256205 Number of permutations in S_n that avoid the pattern 34215.
%H A256205 Anthony Guttmann, <a href="/A256205/b256205.txt">Table of n, a(n) for n = 0..27</a>
%H A256205 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 A256205 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 A256205 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256205     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256205     psn = Permutations[Range[n]]},
%t A256205    For[i = 1, i <= Length[lpat], i++,
%t A256205     p = lpat[[i]];
%t A256205     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256205     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256205 Table[avoid[n, {3, 4, 2, 1, 5}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256205 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256205 Cf. A099952.
%K A256205 nonn
%O A256205 0,3
%A A256205 _N. J. A. Sloane_, Mar 19 2015
%E A256205 More terms from _Anthony Guttmann_, Sep 29 2021