A028107 Expansion of 1/((1-3x)(1-9x)(1-11x)(1-12x)).

1, 35, 790, 14630, 242011, 3723545, 54492880, 769001660, 10558544821, 141919432655, 1875649181770, 24453637571090, 315271616180431, 4027179810711365, 51043597496835460, 642723844104282920

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (35,-435,2205,-3564).

Formula

a(n) = (16*12^(n+3) - 27*11^(n+3) + 12*9^(n+3) - 3^(n+3))/432 = (1/16)*(-3^n + 3^n*4^(n+5) + 4*9^(n+2) - 11^(n+3)). - Yahia Kahloune, May 31 2013

a(n) = 35*a(n-1) - 435*a(n-2) + 2205*a(n-3) - 3564*a(n-4) for n > 3; a(0)=1, a(1)=35, a(2)=790, a(3)=14630. - Vincenzo Librandi, Jul 17 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 9 x) (1 - 11 x)(1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 17 2013 *)
LinearRecurrence[{35, -435, 2205, -3564}, {1, 35, 790, 14630}, 20] (* Harvey P. Dale, Jul 31 2020 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-9*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 35, 790, 14630]; [n le 4 select I[n] else 35*Self(n-1)-435*Self(n-2)+2205*Self(n-3)-3564*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 17 2013

Crossrefs

Sequence in context: A028189 A028162 A028160 * A066553 A137309 A028024

Adjacent sequences: A028104 A028105 A028106 * A028108 A028109 A028110

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved