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

0,3

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

Crossrefs

Sequence in context: A177519 A214762 A141254 * A216879 A372527 A138020

Adjacent sequences: A366703 A366704 A366705 * A366707 A366708 A366709

Keyword

nonn

Author

Jay Pantone, Oct 17 2023

Status

approved