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 A016130 #36 Mar 27 2025 16:11:28
%S A016130 1,9,67,477,3355,23517,164683,1152909,8070619,56494845,395464939,
%T A016130 2768256621,19377800443,135644611293,949512295435,6646586100813,
%U A016130 46526102771227,325682719529661,2279779036969771,15958453259312685,111709172816237371,781964209715758749,5473749468014505547
%N A016130 Expansion of g.f. 1/((1-2*x)*(1-7*x)).
%H A016130 Vincenzo Librandi, <a href="/A016130/b016130.txt">Table of n, a(n) for n = 0..200</a>
%H A016130 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-14).
%F A016130 a(n) = (7^(n+1) - 2^(n+1))/5. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 06 2005
%F A016130 a(n) = 7*a(n-1) + 2^n, a(0)=1. - _Vincenzo Librandi_, Jun 24 2013
%F A016130 From _Elmo R. Oliveira_, Mar 27 2025: (Start)
%F A016130 E.g.f.: exp(2*x)*(7*exp(5*x) - 2)/5.
%F A016130 a(n) = A190540(n+1)/5.
%F A016130 a(n) = 9*a(n-1) - 14*a(n-2). (End)
%e A016130 1/((1-2*x)*(1-7*x)) = 1 + 9*x + 67*x^2 + 477*x^3 + 3355*x^4 + 23517*x^5 + 164683*x^6 + ...
%t A016130 Join[{a=1,b=9},Table[c=9*b-14*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t A016130 CoefficientList[Series[1 /((1 - 2 x) (1 - 7 x)), {x, 0, 200}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)
%o A016130 (Sage) [lucas_number1(n,9,14) for n in range(1, 20)] # _Zerinvary Lajos_, Apr 23 2009
%o A016130 (Sage) [(7^n - 2^n)/5 for n in range(1,20)] # _Zerinvary Lajos_, Jun 04 2009
%o A016130 (PARI) Vec(1/((1-2*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012
%o A016130 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x) (1-7*x)))); // _Vincenzo Librandi_, Jun 24 2013
%Y A016130 Cf. A190540.
%K A016130 nonn,easy
%O A016130 0,2
%A A016130 _N. J. A. Sloane_