A174195 Number of permutations of 1..n that almost avoid 231.

1, 1, 2, 6, 24, 111, 531, 2519, 11726, 53547, 240448, 1064608, 4658952, 20192022, 86807865, 370665585, 1573606410, 6647552115, 27962334180, 117185243340, 489508952160, 2038937744610, 8471179017990, 35115582053214, 145269385076124, 599866065025406, 2472955722033776, 10179494703130704, 41844811399520752, 171796056971896588

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

R. Brignall et al., Almost avoiding permutations, Discrete Math., 309 (2009), 6626-6631.

Formula

G.f.: (1-5*x-6*x^2 + 45*x^3-24*x^4-(1 + x-4*x^2 + x^3)*(1-4*x)^(3/2))/(-2*x^2*(1-4*x)^(3/2)).

a(n) ~ 2^(2*n-2)*sqrt(n)/sqrt(Pi). - Vaclav Kotesovec, Aug 23 2014

Conjecture: 2*(n+2)*(2013*n^2-10435*n+41550)*a(n) +(4026*n^3 -128025*n^2 +34955*n+59010)*a(n-1) -2 *(2*n-5)*(20130*n^2 -110855*n +93819) *a(n-2)=0. - R. J. Mathar, Jun 14 2016

Mathematica

CoefficientList[Series[(1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2)), {x, 0, 50}], x] (* G. C. Greubel, Mar 22 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2))) \\ G. C. Greubel, Mar 22 2017

Crossrefs

Cf. A174193.

Sequence in context: A138020 A046646 A342284 * A274378 A391301 A177521

Adjacent sequences: A174192 A174193 A174194 * A174196 A174197 A174198

Keyword

nonn,changed

Author

N. J. A. Sloane, Nov 26 2010

Status

approved