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A256208 Number of permutations in S_n that avoid the pattern 52341.

%I A256208 #21 Sep 29 2021 02:43:28
%S A256208 1,1,2,6,24,119,694,4582,33325,261863,2192390,19358590,178904675,
%T A256208 1720317763,17132629082,176055309619,1861037944163,20185165186517,
%U A256208 224150069984572,2543698932578158,29451619807433107,347417296695040510,4170088041714300134,50874753262007210667
%N A256208 Number of permutations in S_n that avoid the pattern 52341.
%H A256208 Anthony Guttmann, <a href="/A256208/b256208.txt">Table of n, a(n) for n = 0..23</a>
%H A256208 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 A256208 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 A256208 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256208     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256208     psn = Permutations[Range[n]]},
%t A256208    For[i = 1, i <= Length[lpat], i++,
%t A256208     p = lpat[[i]];
%t A256208     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256208     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256208 Table[avoid[n, {5, 2, 3, 4, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256208 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256208 Cf. A099952.
%K A256208 nonn
%O A256208 0,3
%A A256208 _N. J. A. Sloane_, Mar 19 2015
%E A256208 More terms from _Anthony Guttmann_, Sep 29 2021