A020979 Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)).

1, 29, 563, 9145, 134211, 1845249, 24249163, 308352185, 3824765171, 46535545969, 557596038363, 6599196683625, 77316285612931, 898280118486689, 10363489117309163, 118857642802045465, 1356308170915657491

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (29,-278,880).

Formula

a(0)=1, a(1)=29, a(2)=563; for n>2, a(n) = 29*a(n-1)-278*a(n-2) + 880*a(n-3). - Harvey P. Dale, Dec 19 2012

a(n) = (2*11^(n+2) - 3*10^(n+2) + 8^(n+2))/6. - Yahia Kahloune, Jun 30 2013

a(0)=1, a(1)=29; for n>1, a(n) = 21*a(n-1) -110*a(n-2) +8^(n-1). - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - 8 x) (1 - 10 x) (1 - 11 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{29, -278, 880}, {1, 29, 563}, 30] (* Harvey P. Dale, Dec 19 2012 *)

Prog

(Magma) I:=[1, 29, 563]; [n le 3 select I[n] else 29*Self(n-1)-278*Self(n-2)+880*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-10*x)*(1-11*x)))); // Vincenzo Librandi, Jul 08 2013
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-10*x)*(1-11*x))) \\ G. C. Greubel, Feb 09 2018

Crossrefs

Sequence in context: A026241 A024443 A024435 * A025985 A020978 A023948

Adjacent sequences: A020976 A020977 A020978 * A020980 A020981 A020982

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved