A020977 Expansion of 1/((1-8*x)*(1-9*x)*(1-11*x)).

1, 28, 525, 8240, 116921, 1555428, 19795525, 244020280, 2937425841, 34724726828, 404763120125, 4666104381120, 53319258206761, 604990586218228, 6825603208406325, 76653180504610760, 857610367436699681, 9565794278591213628, 106430473594100486125

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (28,-259,792).

Formula

a(n) = (11^(n+2) - 3*9^(n+2) + 2*8^(n+2))/6. - Yahia Kahloune, Jun 30 2013

a(0)=1, a(1)=28, a(2)=525; for n>2, a(n) = 28*a(n-1) -259*a(n-2) +792*a(n-3). - Vincenzo Librandi, Jul 05 2013

a(n) = 20*a(n-1) -99*a(n-2) + 8^n. - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)
LinearRecurrence[{28, -259, 792}, {1, 28, 525}, 20] (* Harvey P. Dale, Mar 30 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 28, 525]; [n le 3 select I[n] else 28*Self(n-1)-259*Self(n-2)+792*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 05 2013
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-9*x)*(1-11*x))) \\ G. C. Greubel, Feb 09 2018

Crossrefs

Sequence in context: A024440 A024347 A025984 * A020973 A023947 A020972

Adjacent sequences: A020974 A020975 A020976 * A020978 A020979 A020980

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved