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A256206 Number of permutations in S_n that avoid the pattern 42315.

%I A256206 #21 Sep 29 2021 02:40:35
%S A256206 1,1,2,6,24,119,694,4581,33287,260967,2175379,19072271,174426353,
%T A256206 1653484169,16165513608,162344264849,1669261805697,17526017429722,
%U A256206 187472773174466,2039233971499931,22520066337196663,252141732452056894,2858721279079666465,32786666580814894741
%N A256206 Number of permutations in S_n that avoid the pattern 42315.
%H A256206 Anthony Guttmann, <a href="/A256206/b256206.txt">Table of n, a(n) for n = 0..26</a>
%H A256206 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 A256206 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 A256206 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256206     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256206     psn = Permutations[Range[n]]},
%t A256206    For[i = 1, i <= Length[lpat], i++,
%t A256206     p = lpat[[i]];
%t A256206     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256206     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256206 Table[avoid[n, {4, 2, 3, 1, 5}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256206 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256206 Cf. A099952.
%K A256206 nonn
%O A256206 0,3
%A A256206 _N. J. A. Sloane_, Mar 19 2015
%E A256206 More terms from _Anthony Guttmann_, Sep 29 2021