%I #17 Sep 08 2022 08:44:44
%S 1,18,220,2280,21616,194208,1685440,14290560,119232256,983566848,
%T 8047836160,65462691840,530198327296,4280634482688,34479631482880,
%U 277245459333120,2226418414452736,17862092934217728
%N Expansion of 1/((1-4x)(1-6x)(1-8x)).
%H Vincenzo Librandi, <a href="/A019333/b019333.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 (18,-104,192).
%F a(n) = 2*4^n -9*6^n +8*8^n. - _R. J. Mathar_, Jun 29 2013
%F a(0)=1, a(1)=18, a(2)=220; for n>2, a(n) = 18*a(n-1) -104*a(n-2) +192*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 14*a(n-1) -48*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 02 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%o (PARI) Vec(1/((1-4*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 18, 220]; [n le 3 select I[n] else 18*Self(n-1)-104*Self(n-2)+192*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013
%Y Equals 2^n * A016269.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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