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 A016138 #42 Nov 14 2024 05:46:27
%S A016138 1,10,79,580,4141,29230,205339,1439560,10083481,70604050,494287399,
%T A016138 3460188940,24221854021,169554572470,1186886790259,8308221880720,
%U A016138 58157596211761,407103302622490,2849723505777919,19948065702706900,139636463405732701,977455254300482110,6842186811484434379,47895307774534219480
%N A016138 Expansion of 1/((1-3*x)*(1-7*x)).
%H A016138 Vincenzo Librandi, <a href="/A016138/b016138.txt">Table of n, a(n) for n = 0..1000</a>
%H A016138 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-21).
%F A016138 a(n) = (7^(n+1) - 3^(n+1))/4. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
%F A016138 a(n) = 10*a(n-1) - 21*a(n-2). - _Philippe Deléham_, Jan 01 2009
%F A016138 G.f.: x/(1-10*x+21*x^2). - _Zerinvary Lajos_, Apr 26 2009
%F A016138 E.g.f.: (d/dx)(exp(3*x)*(exp(4*x)-1)/4) = exp(3*x)*(7*exp(4*x) - 3)/4. - _Wolfdieter Lang_, Apr 13 2017
%t A016138 Table[(7^(n+1) - 3^(n+1))/4, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t A016138 CoefficientList[Series[1/((1-3x)(1-7x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-21},{1,10},30] (* _Harvey P. Dale_, Nov 07 2014 *)
%o A016138 (Sage) [lucas_number1(n,10,21) for n in range(1, 30)] # _Zerinvary Lajos_, Apr 26 2009
%o A016138 (Magma) [(7^(n+1)-3^(n+1))/4: n in [0..30]]; // _Vincenzo Librandi_, Oct 09 2011
%o A016138 (PARI) Vec(1/((1-3*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A016138 Cf. Column k=1 of A225469.
%K A016138 nonn,easy
%O A016138 0,2
%A A016138 _N. J. A. Sloane_