A366706 Number of permutations of length n avoiding the permutations 13452, 13542, 14253, 14352, 14532, 15243, 15342, 15432, 24153, and 25143.
1, 1, 2, 6, 24, 110, 540, 2772, 14704, 79974, 443592, 2499596, 14268740, 82339972, 479549860, 2815097792, 16639456452, 98947148126, 591537712636, 3553227623724, 21434384242112, 129796819639908, 788724906697704, 4807951095533744, 29393378297989024
Offset: 0
Keywords
Links
- Jay Pantone, Table of n, a(n) for n = 0..100
- Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Combinatorial Exploration: An algorithmic framework for enumeration, arXiv:2202.07715 [math.CO], 2022.
- Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, PermPAL Database
- Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
Formula
G.f. satisfies the minimal polynomial (4*x-1)*F(x)^4+(-16*x+6)*F(x)^3+(x^2+24*x-13)*F(x)^2+(-16*x+12)*F(x)+4*x-4 = 0.
a(n) ~ sqrt((2 - 8*s + (12 + r)*s^2 - 8*s^3 + 2*s^4) / (2*Pi*(-13 + r^2 + 24*r*(-1 + s)^2 + 18*s - 6*s^2))) / (n^(3/2) * r^(n - 1/2)), where r = 0.15337200146837895871745857265131731893709232... and s = 1.329726282094188543969222211385207173949290634... are positive real roots of the system of equations r*(4*(-1 + s)^4 + r*s^2) = (2 - 3*s + s^2)^2, 6 + 8*r*(-1 + s)^3 + r^2*s + 9*s^2 = 13*s + 2*s^3. - Vaclav Kotesovec, Jul 22 2024