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%I #19 Apr 06 2023 09:11:03
%S 1,31,645,11255,177821,2636991,37440565,515147335,6923011341,
%T 91364030351,1188608942885,15286543614615,194762842152061,
%U 2462271368182111,30927944350627605,386358083836485095
%N Expansion of 1/((1-8*x)*(1-11*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A020981/b020981.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 (31,-316,1056).
%F a(n) = 16*8^n/3 -121*11^n/3 +36*12^n. - _R. J. Mathar_, Jul 01 2013
%F a(0)=1, a(1)=31, a(2)=645; for n>2, a(n) = 31*a(n-1) -316*a(n-2) +1056*a(n-3). - _Vincenzo Librandi_, Jul 05 2013
%F a(n) = 23*a(n-1) -132*a(n-2) +8^n. - _Vincenzo Librandi_, Jul 05 2013
%t CoefficientList[Series[1 / ((1 - 8 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)
%t LinearRecurrence[{31,-316,1056},{1,31,645},20] (* _Harvey P. Dale_, Apr 06 2023 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 31, 645]; [n le 3 select I[n] else 31*Self(n-1)-316*Self(n-2)+1056*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 05 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-11*x)*(1-12*x))) \\ _G. C. Greubel_, Feb 09 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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