%I #26 Sep 08 2022 08:44:45
%S 1,29,565,9245,137221,1915949,25677205,334395965,4265954341,
%T 53604494669,666045061045,8206250792285,100467119521861,
%U 1224084180206189,14859716922480085,179888148281902205
%N Expansion of 1/((1-8*x)*(1-9*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A020978/b020978.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,-276,864).
%F a(n) = (12^(n+2) - 4*9^(n+2) + 3*8^(n+2))/12. - _Yahia Kahloune_, Jun 30 2013
%F a(0)=1, a(1)=29, a(2)=565; for n>2, a(n) = 29*a(n-1) -276*a(n-2) +864*a(n-3). - _Vincenzo Librandi_, Jul 05 2013
%F a(n) = 21*a(n-1) -108*a(n-2) +8^n. - _Vincenzo Librandi_, Jul 05 2013
%t CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)
%t LinearRecurrence[{29, -276, 864}, {1, 29, 565}, 16] (* _Robert G. Wilson v_, Jul 05 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-12*x)))); /* or */ I:=[1, 29, 565]; [n le 3 select I[n] else 29*Self(n-1)-276*Self(n-2)+864*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)*(1-12*x))) \\ _G. C. Greubel_, Feb 09 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_