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%I #10 Sep 08 2022 08:44:45
%S 1,16,173,1604,13833,115032,938821,7588108,61024865,489508448,
%T 3921394269,31392726612,251228899897,2010181938664,16082865641717,
%U 128668587186716,1029371410275729,8235062327044080,65880863376836365
%N Expansion of 1/((1-x)(1-3x)(1-4x)(1-8x)).
%H Vincenzo Librandi, <a href="/A021374/b021374.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 (16,-83,164,-96).
%F a(0)=1, a(1)=16; for n>1, a(n) = 12*a(n-1) -32*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 09 2013
%F a(0)=1, a(1)=16, a(2)=173, a(3)=1604; for n>3, a(n) = 16*a(n-1) -83*a(n-2) +164*a(n-3) -96*a(n-4). - _Vincenzo Librandi_, Jul 09 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 09 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-8*x)))); /* or */ I:=[1, 16, 173, 1604]; [n le 4 select I[n] else 16*Self(n-1)-83*Self(n-2)+164*Self(n-3)-96*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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