OFFSET
2,3
COMMENTS
Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x).
Is this row 2 of the convolution array A213819? - Clark Kimberling, Jul 04 2012
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243 [math.CO], 2012.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
For n>=4, a(n) = (n-3)*A212342(n-1).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>7. - Colin Barker, Jul 10 2015
G.f.: -x^4*(2*x-5) / (x-1)^4. - Colin Barker, Jul 10 2015
From Amiram Eldar, Apr 03 2022: (Start)
Sum_{n>=4} 1/a(n) = 23/72.
Sum_{n>=4} (-1)^n/a(n) = 4*log(2)/3 - 55/72. (End)
MATHEMATICA
QQ0[t, x] = (1 - (1-4*x*t)^(1/2)) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); CoefficientList[Coefficient[Simplify[Series[QQ3[t, x], {t, 0, 35}]], x], t] (* Robert Price, Jun 04 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 0, 5, 18}, 60] (* Harvey P. Dale, Mar 15 2018 *)
PROG
(PARI) Vec(-x^4*(2*x-5)/(x-1)^4 + O(x^100)) \\ Colin Barker, Jul 10 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 09 2012
EXTENSIONS
a(10)-a(35) from Robert Price, Jun 02 2012
Entry revised by N. J. A. Sloane, Sep 10 2016
STATUS
approved