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

%I #26 Sep 08 2022 08:44:45

%S 1,28,525,8240,116921,1555428,19795525,244020280,2937425841,

%T 34724726828,404763120125,4666104381120,53319258206761,

%U 604990586218228,6825603208406325,76653180504610760,857610367436699681,9565794278591213628,106430473594100486125

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

%H Vincenzo Librandi, <a href="/A020977/b020977.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (28,-259,792).

%F a(n) = (11^(n+2) - 3*9^(n+2) + 2*8^(n+2))/6. - _Yahia Kahloune_, Jun 30 2013

%F 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

%F a(n) = 20*a(n-1) -99*a(n-2) + 8^n. - _Vincenzo Librandi_, Jul 05 2013

%t CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)

%t LinearRecurrence[{28,-259,792},{1,28,525},20] (* _Harvey P. Dale_, Mar 30 2018 *)

%o (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

%o (PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-9*x)*(1-11*x))) \\ _G. C. Greubel_, Feb 09 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_