A366706 - OEIS

%I #20 Jul 22 2024 15:50:38

%S 1,1,2,6,24,110,540,2772,14704,79974,443592,2499596,14268740,82339972,

%T 479549860,2815097792,16639456452,98947148126,591537712636,

%U 3553227623724,21434384242112,129796819639908,788724906697704,4807951095533744,29393378297989024

%N Number of permutations of length n avoiding the permutations 13452, 13542, 14253, 14352, 14532, 15243, 15342, 15432, 24153, and 25143.

%H Jay Pantone, <a href="/A366706/b366706.txt">Table of n, a(n) for n = 0..100</a>

%H Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://arxiv.org/abs/2202.07715">Combinatorial Exploration: An algorithmic framework for enumeration</a>, arXiv:2202.07715 [math.CO], 2022.

%H Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://permpal.com/perms/basis/02341_02431_03142_03241_03421_04132_04231_04321_13042_14032/">PermPAL Database</a>

%H Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://doi.org/10.37236/12686">Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding</a>, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); <a href="https://arxiv.org/abs/2312.07716">arXiv preprint</a>, arXiv:2312.07716 [math.CO], 2023.

%F 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.

%F 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

%K nonn

%O 0,3

%A _Jay Pantone_, Oct 17 2023