A212339 Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(0,0,3,0)(x).

5, 19, 61, 188, 523, 1387, 3565, 8888, 21674, 51928, 122522, 285434, 657789, 1501617, 3399771, 7641564, 17064957, 37889229, 83688437, 183979390, 402729040, 878129096, 1907861044, 4131449572, 8919397717, 19201879583, 41230101641, 88313236636, 188733236543

Offset

4,1

Comments

Conjecture: satisfies a linear recurrence having signature (3, 0, 1, -12, -3, 1, 18, 12, 8). - Harvey P. Dale, Sep 03 2021

Links

Table of n, a(n) for n=4..32.

S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243, 2012

Formula

Empirical g.f.: -x^4*(4*x^2+4*x+5) / ((2*x-1)^3*(x^2+x+1)^3). - Colin Barker, Jul 22 2013

Mathematica

QQQ3[t, x] = 2 /(1+(t*x-t)*(1+t+2*t^2) + ((1 + (t*x - t)*(1 + t + 2*t^2))^2 - 4*t*x)^(1/2)); CoefficientList[Coefficient[Series[QQQ3[t, x], {t, 0, 22}], x], t] (* Robert Price, Jun 05 2012 *)

Crossrefs

Sequence in context: A000342 A189427 A355492 * A072111 A173627 A295288

Adjacent sequences: A212336 A212337 A212338 * A212340 A212341 A212342

Keyword

nonn

Author

N. J. A. Sloane, May 09 2012

Extensions

a(10)-a(22) from Robert Price, Jun 04 2012

Status

approved