cp's OEIS Frontend

A256203 Number of permutations in S_n that avoid the pattern 43251.

%I A256203 #21 Sep 29 2021 02:36:51
%S A256203 1,1,2,6,24,119,694,4581,33283,260805,2171393,18994464,173094540,
%T A256203 1632480259,15851668551,157824649955,1605839173312,16652321922596,
%U A256203 175596537163347,1879357191026029,20382942631855557,223719376672365073,2482094083780961295,27808544385768051233
%N A256203 Number of permutations in S_n that avoid the pattern 43251.
%H A256203 Anthony Guttmann, <a href="/A256203/b256203.txt">Table of n, a(n) for n = 0..27</a>
%H A256203 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 A256203 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 A256203 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256203     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256203     psn = Permutations[Range[n]]},
%t A256203    For[i = 1, i <= Length[lpat], i++,
%t A256203     p = lpat[[i]];
%t A256203     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256203     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256203 Table[avoid[n, {4, 3, 2, 5, 1}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256203 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256203 Cf. A099952.
%K A256203 nonn
%O A256203 0,3
%A A256203 _N. J. A. Sloane_, Mar 19 2015
%E A256203 More terms from _Anthony Guttmann_, Sep 29 2021