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
KEYWORD
nonn
AUTHOR
Jay Pantone, Oct 17 2023
STATUS
approved