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%I #15 Sep 08 2022 08:44:44
%S 1,23,373,5279,69853,890519,11105221,136616783,1666241005,20209628615,
%T 244233494869,2944545727487,35444499573757,426213603230711,
%U 5121600110316517,61515496310530991,738636315663280909
%N Expansion of 1/((1-3x)(1-8x)(1-12x)).
%H Vincenzo Librandi, <a href="/A018071/b018071.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (23,-156,288).
%F a(0)=1, a(1)=23, a(2)=373; for n>2, a(n) = 23*a(n-1) -156*a(n-2) +288*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 20*a(n-1) -96*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = (5*12^(n+2) - 9*8^(n+2) + 4*3^(n+2))/180. [_Yahia Kahloune_, Jul 06 2013]
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 8 x) (1 - 12 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%t LinearRecurrence[{23,-156,288},{1,23,373},30] (* _Harvey P. Dale_, Aug 27 2014 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)*(1-12*x)))); * or */ I:=[1, 23, 373]; [n le 3 select I[n] else 23*Self(n-1)-156*Self(n-2)+288*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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