login
A256206
Number of permutations in S_n that avoid the pattern 42315.
1
1, 1, 2, 6, 24, 119, 694, 4581, 33287, 260967, 2175379, 19072271, 174426353, 1653484169, 16165513608, 162344264849, 1669261805697, 17526017429722, 187472773174466, 2039233971499931, 22520066337196663, 252141732452056894, 2858721279079666465, 32786666580814894741
OFFSET
0,3
LINKS
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.
MATHEMATICA
avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
psn = Permutations[Range[n]]},
For[i = 1, i <= Length[lpat], i++,
p = lpat[[i]];
AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {4, 2, 3, 1, 5}], {n, 0, 8}] (* Robert Price, Mar 27 2020 *)
CROSSREFS
Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.
Sequence in context: A256204 A256205 A116485 * A052397 A047889 A256207
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 19 2015
EXTENSIONS
More terms from Anthony Guttmann, Sep 29 2021
STATUS
approved