This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016136 #33 Mar 08 2025 18:19:23
%S A016136 1,14,172,2072,24880,298592,3583168,42998144,515977984,6191736320,
%T A016136 74300836864,891610044416,10699320537088,128391846453248,
%U A016136 1540702157455360,18488425889497088,221861110674030592,2662333328088498176,31947999937062240256,383375999244747407360,4600511990936969936896
%N A016136 Expansion of 1/((1-2*x)*(1-12*x)).
%H A016136 Vincenzo Librandi, <a href="/A016136/b016136.txt">Table of n, a(n) for n = 0..900</a>
%H A016136 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-24).
%F A016136 a(n) = (12^n - 2^n)/10 for n > 0. - _Zerinvary Lajos_, Jun 05 2009
%F A016136 From _Vincenzo Librandi_, Oct 09 2011: (Start)
%F A016136 a(n) = 2^n*(6^(n+1) - 1)/5.
%F A016136 a(n) = 14*a(n-1) - 24*a(n-2). (End)
%F A016136 a(n) = Sum_{i=0..n} 2^(n+i)*3^i. - _Bruno Berselli_, Aug 28 2013
%F A016136 E.g.f.: exp(2*x)*(exp(10*x) - 1)/10. - _Elmo R. Oliveira_, Mar 08 2025
%e A016136 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 A016136 CoefficientList[Series[1/((1 - 2*x)*(1 - 12*x)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Apr 08 2017 *)
%o A016136 (Sage) [(12^n - 2^n)/10 for n in range(1,18)] # _Zerinvary Lajos_, Jun 05 2009
%o A016136 (Magma) [2^n*(6^(n+1)-1)/5: n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o A016136 (PARI) Vec(1/((1-2*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016136 (Magma) [&+[2^(n+i)*3^i: i in [0..n]]: n in [0..20]]; // _Bruno Berselli_, Aug 28 2013
%K A016136 nonn,easy
%O A016136 0,2
%A A016136 _N. J. A. Sloane_