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 A016150 #39 Mar 26 2025 13:28:49
%S A016150 1,11,93,715,5261,37851,269053,1899755,13363821,93808891,657710813,
%T A016150 4608169995,32273967181,225984879131,1582162589373,11076211867435,
%U A016150 77537778039341,542781626144571,3799540102488733,26597055595328075,186180488678924301,1303267818798981211,9122892323778912893
%N A016150 Expansion of g.f. 1/((1-4*x)*(1-7*x)).
%H A016150 Vincenzo Librandi, <a href="/A016150/b016150.txt">Table of n, a(n) for n = 0..200</a>
%H A016150 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-28).
%F A016150 From _Barry E. Williams_, Jan 13 2000: (Start)
%F A016150 a(n) = (7^(n+1) - 4^(n+1))/3.
%F A016150 a(n) = 11*a(n-1) - 28*a(n-2) for n>0, a(0)=1. (End)
%F A016150 a(n) = Sum_{k=0..n} 7^k*4^(n-k). - _Bruno Berselli_, Aug 07 2013
%F A016150 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A016150 E.g.f.: exp(4*x)*(7*exp(3*x) - 4)/3.
%F A016150 a(n) = A190542(n+1)/3. (End)
%t A016150 Join[{a=1,b=11},Table[c=11*b-28*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2011 *)
%t A016150 CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)
%t A016150 LinearRecurrence[{11,-28},{1,11},20] (* _Harvey P. Dale_, Mar 11 2020 *)
%o A016150 (Sage) [lucas_number1(n,11,28) for n in range(1, 20)] # _Zerinvary Lajos_, Apr 27 2009
%o A016150 (PARI) Vec(1/((1-4*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016150 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)))); // _Vincenzo Librandi_, Jun 24 2013
%Y A016150 Cf. A190542.
%K A016150 nonn,easy
%O A016150 0,2
%A A016150 _N. J. A. Sloane_