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 A016162 #24 Nov 10 2024 05:18:15
%S A016162 1,13,129,1157,9881,82173,673009,5462197,44088201,354658733,
%T A016162 2847035489,22825112037,182845036921,1463980998493,11717951503569,
%U A016162 93774129606677,750345624744041,6003527937405453,48032038196509249
%N A016162 Expansion of 1/((1-5*x)*(1-8*x)).
%H A016162 G. C. Greubel, <a href="/A016162/b016162.txt">Table of n, a(n) for n = 0..1000</a>
%H A016162 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-40).
%F A016162 a(n) = (8^(n+1) - 5^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
%F A016162 a(0)=1, a(n) = 8*a(n-1) + 5^n. - _Vincenzo Librandi_, Feb 09 2011
%F A016162 a(0)=1, a(1)=13, a(n) = 13*a(n-1) - 40*a(n-2). - _Harvey P. Dale_, Feb 02 2015
%F A016162 E.g.f.: (1/3)*(-5*exp(5*x) + 8*exp(8*x)). - _G. C. Greubel_, Nov 09 2024
%t A016162 Table[(8^(n+1)-5^(n+1))/3, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A016162 CoefficientList[Series[1/((1-5x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[ {13,-40},{1,13},30] (* _Harvey P. Dale_, Feb 02 2015 *)
%o A016162 (PARI) Vec(1/((1-5*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016162 (Magma) [n le 2 select 13^(n-1) else 13*Self(n-1) -40*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 09 2024
%o A016162 (SageMath)
%o A016162 A016162=BinaryRecurrenceSequence(13,-40,1,13)
%o A016162 [A016162(n) for n in range(31)] # _G. C. Greubel_, Nov 09 2024
%Y A016162 Cf. A016161.
%K A016162 nonn,easy
%O A016162 0,2
%A A016162 _N. J. A. Sloane_