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%I #27 Sep 08 2022 08:44:40
%S 1,14,172,2072,24880,298592,3583168,42998144,515977984,6191736320,
%T 74300836864,891610044416,10699320537088,128391846453248,
%U 1540702157455360,18488425889497088,221861110674030592
%N Expansion of 1/((1-2*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A016136/b016136.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-24).
%F a(n) = (12^n - 2^n)/10 for n>0. [_Zerinvary Lajos_, Jun 05 2009]
%F a(n) = 2^n*(6^(n+1)-1)/5 = 14*a(n-1)-24*a(n-2). - _Vincenzo Librandi_, Oct 09 2011
%F a(n) = Sum_{i=0..n} 2^(n+i)*3^i. [_Bruno Berselli_, Aug 28 2013]
%e For n=6, a(6) = 2^6+2^7*3+2^8*3^2+2^9*3^3+2^10*3^4+2^11*3^5+2^12*3^6 = 3583168. [_Bruno Berselli_, Aug 28 2013]
%t CoefficientList[Series[1/((1 - 2*x)*(1 - 12*x)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Apr 08 2017 *)
%o (Sage) [(12^n - 2^n)/10 for n in range(1,18)] /* _Zerinvary Lajos_, Jun 05 2009 */
%o (Magma) [2^n*(6^(n+1)-1)/5: n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o (PARI) Vec(1/((1-2*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) [&+[2^(n+i)*3^i: i in [0..n]]: n in [0..20]]; // _Bruno Berselli_, Aug 28 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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