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%I #22 Sep 08 2022 08:44:45
%S 1,29,563,9145,134211,1845249,24249163,308352185,3824765171,
%T 46535545969,557596038363,6599196683625,77316285612931,
%U 898280118486689,10363489117309163,118857642802045465,1356308170915657491
%N Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)).
%H Vincenzo Librandi, <a href="/A020979/b020979.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 (29,-278,880).
%F 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
%F a(n) = (2*11^(n+2) - 3*10^(n+2) + 8^(n+2))/6. - _Yahia Kahloune_, Jun 30 2013
%F 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
%t 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 *)
%o (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
%o (PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-10*x)*(1-11*x))) \\ _G. C. Greubel_, Feb 09 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_