OFFSET
0,3
COMMENTS
a(n) is also the number of permutations in S_n that avoid the pattern 21453 or any of its symmetries. The Wilf class consists of 16 permutations. - David Bevan, Jun 17 2021
LINKS
Yonah Biers-Ariel, Table of n, a(n) for n = 0..37
Yonah Biers-Ariel, Julia program to compute terms
Miklos Bona, The limit of a Stanley-Wilf sequence is not always rational, and layered patterns beat monotone patterns, arXiv:math/0403502 [math.CO], 2004.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.
FORMULA
Conjecture: a(n) + A158423(n) = n!. - Benedict W. J. Irwin, Mar 15 2016
The conjecture is true: All that is needed is to show that 23145 is Wilf-equivalent to 31245, but that’s obvious since they are inverses. - Doron Zeilberger and Yonah Biers-Ariel, Feb 26 2019
The exponential growth rate is 9+4*sqrt(2). See [Bona 2004]. - David Bevan, Jun 17 2021
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, {1, 2, 4, 5, 3}], {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. - N. J. A. Sloane, Mar 19 2015
KEYWORD
nonn
AUTHOR
Zvezdelina Stankova (stankova(AT)mills.edu), Mar 19 2006
EXTENSIONS
More terms from the Zvezdelina Stankova-Frenkel and Julian West paper. - N. J. A. Sloane, Mar 19 2015
More terms from Doron Zeilberger and Yonah Biers-Ariel, Feb 26 2019
More terms from Yonah Biers-Ariel, Mar 04 2019
STATUS
approved