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%I #25 Sep 08 2022 08:44:44
%S 1,17,197,1945,17661,152817,1284277,10599305,86485421,700600417,
%T 5649437157,45422860665,364536479581,2922126916817,23406459170837,
%U 187399966290025,1499945489904141,12003309897022017,96045277784597317
%N Expansion of 1/((1-4x)(1-5x)(1-8x)).
%H Vincenzo Librandi, <a href="/A018250/b018250.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-92,160).
%F G.f.: 1/((1-4*x)*(1-5*x)*(1-8*x)).
%F a(n) = (3*4^(n+1)-5^(n+2)+2*8^(n+1))/3. - _Bruno Berselli_, Apr 05 2011
%F a(n) = 17*a(n-1) - 92*a(n-2) + 160*a(n-3). - _Wesley Ivan Hurt_, Sep 04 2022
%t CoefficientList[Series[1/((1-4x)(1-5x)(1-8x)),{x,0,20}],x] (* _Harvey P. Dale_, Apr 05 2011 *)
%t Table[(3 4^(n + 1) - 5^(n + 2) + 2 8^(n + 1)) / 3, {n, 0, 50}] (* _Vincenzo Librandi_, Jun 20 2013 *)
%o (Magma) [(3*4^(n+1)-5^(n+2)+2*8^(n+1))/3: n in [0..30]]; // _Vincenzo Librandi_, Jun 20 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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