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 A190994 #37 Oct 26 2022 20:00:54
%S A190994 27,2,29,31,60,91,151,242,393,635,1028,1663,2691,4354,7045,11399,
%T A190994 18444,29843,48287,78130,126417,204547,330964,535511,866475,1401986,
%U A190994 2268461,3670447,5938908,9609355,15548263,25157618,40705881,65863499
%N A190994 a(n) = a(n-1) + a(n-2), for n>=2, with a(0)=27, a(1)=2.
%C A190994 Fibonacci sequence beginning 27, 2.
%H A190994 Vincenzo Librandi, <a href="/A190994/b190994.txt">Table of n, a(n) for n = 0..202</a>
%H A190994 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A190994 G.f.: (27-25*x)/(1-x-x^2). - _Harvey P. Dale_, Jun 19 2011
%F A190994 a(n) = (27/2)*( ((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n ) + (23/10)*sqrt(5)*( ((1-sqrt(5))/2)^n - ((1+sqrt(5))/2)^n ). - _Antonio Alberto Olivares_, Jun 19 2011, corrected by _Klaus Brockhaus_, Jun 20 2011
%F A190994 a(n) = 2*Fibonacci(n) + 27*Fibonacci(n-1). - _Charles R Greathouse IV_, Jun 20 2011
%F A190994 a(n) = 2*LucasL(n) + 25*Fibonacci(n-1). - _G. C. Greubel_, Oct 26 2022
%p A190994 a:= n-> (<<0|1>, <1|1>>^n. <<27, 2>>)[1,1]:
%p A190994 seq(a(n), n=0..50); # _Alois P. Heinz_, Nov 18 2018
%t A190994 LinearRecurrence[{1, 1}, {27, 2}, 100]
%t A190994 CoefficientList[Series[(25x-27)/(x^2+x-1),{x,0,100}],x] (* _Harvey P. Dale_, Jun 19 2011 *)
%o A190994 (Magma) [n eq 1 select 27 else n eq 2 select 2 else Self(n-1)+Self(n-2): n in [1..40]]; // _Klaus Brockhaus_, Jun 20 2011
%o A190994 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ 27/2*((1/2+1/2*r)^n+(1/2-1/2*r)^n)+23/10*r*((1/2-1/2*r)^n-(1/2+1/2*r)^n): n in [0..39] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jun 20 2011
%o A190994 (Maxima) makelist(coeff(taylor((25*x-27)/(x^2+x-1), x, 0, n), x, n), n, 0, 33); /* _Bruno Berselli_, Jun 20 2011 */
%o A190994 (PARI) a(n)=27*fibonacci(n-1)+2*fibonacci(n) \\ _Charles R Greathouse IV_, Jun 20 2011
%o A190994 (SageMath) [2*fibonacci(n+1) + 25*fibonacci(n-1) for n in range(101)] # _G. C. Greubel_, Oct 26 2022
%Y A190994 Cf. A000045, A000032, A157681.
%K A190994 nonn,easy,less
%O A190994 0,1
%A A190994 _Vladimir Joseph Stephan Orlovsky_, Jun 06 2011