A212340 G.f.: 1/(1-x-x^2-2*x^3-5*x^4).

1, 1, 2, 5, 14, 28, 62, 143, 331, 738, 1665, 3780, 8576, 19376, 43837, 99265, 224734, 508553, 1151002, 2605348, 5897126, 13347243, 30210075, 68378310, 154768501, 350303176, 792878672, 1794610400, 4061937929, 9193821553, 20809373642, 47100123053, 106606829446, 241294807548

Offset

0,3

Comments

Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,0,4,0)(x).

Links

Table of n, a(n) for n=0..33.

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

Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II, Electronic Journal of Combinatorial Number Theory, Volume 15 #A16. (arXiv:1302.2274)

Anthony Zaleski, Doron Zeilberger, On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts, arXiv:1712.10072 [math.CO], 2017.

Index entries for linear recurrences with constant coefficients, signature (1,1,2,5).

Mathematica

QQQ4[t, x] = 2/(1 +(t*x-t) *(1+t+2*t^2+5*t^3) + ((1+(t*x-t) *(1+t+2*t^2+5*t^3))^2 -4*t*x)^(1/2)); q = Simplify[Series[QQQ4[t, x], {t, 0, 22}]]; CoefficientList[q /. x -> 0, t] (* Robert Price, Jun 04 2012 *)
LinearRecurrence[{1, 1, 2, 5}, {1, 1, 2, 5}, 34] (* Jean-François Alcover, Sep 21 2017 *)

Prog

(PARI) Vec(1/(1-x-x^2-2*x^3-5*x^4) + O(x^100)) \\ Altug Alkan, Nov 01 2015

Crossrefs

Sequence in context: A212346 A194124 A349094 * A304719 A022630 A047133

Adjacent sequences: A212337 A212338 A212339 * A212341 A212342 A212343

Keyword

nonn,easy

Author

N. J. A. Sloane, May 09 2012

Extensions

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

Edited by N. J. A. Sloane, Feb 17 2018

Status

approved