A212347 Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).

14, 56, 144, 300, 550, 924, 1456, 2184, 3150, 4400, 5984, 7956, 10374, 13300, 16800, 20944, 25806, 31464, 38000, 45500, 54054, 63756, 74704, 87000, 100750, 116064, 133056, 151844, 172550, 195300, 220224, 247456, 277134, 309400, 344400, 382284, 423206, 467324, 514800, 565800, 620494, 679056, 741664, 808500, 879750, 955604

Offset: 5

Author

N. J. A. Sloane, May 09 2012

Keywords

• nonn
• easy

Links

• S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243, 2012
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

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]); QQ4[t, x] = (1 + t*(QQ3[t, x] - QQ0[t, x] + t*(QQ2[t, x] - QQ0[t, x]) + (2*t^2*(QQ1[t, x] - QQ0[t, x]))))/(1 - t*QQ0[t, x]); CoefficientList[Coefficient[Simplify[Series[QQ4[t, x], {t, 0, 35}]],x],t] (* Robert Price, Jun 04 2012 *)
Table[(n-4)*(n-3)*(n+1)*(n+2)/6, {n, 5, 50}] (* Jean-François Alcover, Sep 21 2017 *)

Formula

For n>=5, a(n)=(n^2-2n-8)(n^2-2n-3)/6 or a(n)=(n-4)*A212346(n-1).

G.f.: -2*x^5*(2*x^2-7*x+7) / (x-1)^5. - Colin Barker, Jul 22 2013

Extensions

a(10)-a(35) from Robert Price, Jun 02 2012