A213164 Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(4,0,-,0)(x).

1, 9, 51, 235, 966, 3702, 13546, 47994, 166095, 564679, 1893285, 6277677, 20626588, 67260540, 217924068, 702199684, 2251881645, 7191492885, 22882022695, 72568700415, 229473998466, 723725687314, 2277088137966, 7148997642270, 22400192612251, 70060176893427

Offset

5,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 5..1000

S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243 [math.CO], 2012-2014.

Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-33,9).

Formula

From Vaclav Kotesovec, Nov 25 2012: (Start)

a(n) = ((2*n-11)*3^(n-2)+2*n^2-2*n+3)/16

Recurrence: a(n) = 9*a(n-1) - 30*a(n-2) + 46*a(n-3) - 33*a(n-4) + 9*a(n-5)

G.f.: -((1-9*x+30*x^2-46*x^3+33*x^4)/(9*(-1+x)^3*(-1+3*x)^2))

(End)

Mathematica

CCC[t] = (1 - (1 - 4*t)^(1/2))/(2*t); NQ0[t, x] = ((1 + t - t*x) - ((1 + t - t*x)^2 - 4*t)^(1/2))/(2*t); NQ1[t, x] = 1/(1 - t*NQ0[t, x]); NQ2[t, x] = 1/(1 - t*NQ1[t, x]); NQ3[t, x] = 1/(1 - t*NQ2[t, x]); NQ4[t, x] = 1/(1 - t*NQ3[t, x]); CoefficientList[Coefficient[Simplify[Series[NQ4[t, x], {t, 0, 20}]], x], t] (* Robert Price, Jun 06 2012 *)
LinearRecurrence[{9, -30, 46, -33, 9}, {1, 9, 51, 235, 966}, 50] (* Vincenzo Librandi, Nov 25 2012 *)

Prog

(Magma) I:=[1, 9, 51, 235, 966]; [n le 5 select I[n] else 9*Self(n-1) - 30*Self(n-2)+ 46*Self(n-3) - 33*Self(n-4) + 9*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Nov 25 2012

Crossrefs

Sequence in context: A345954 A061178 A246178 * A278135 A097789 A080624

Adjacent sequences: A213161 A213162 A213163 * A213165 A213166 A213167

Keyword

nonn

Author

Robert Price, Jun 06 2012

Status

approved