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 A081005 #34 Jul 02 2025 16:02:01
%S A081005 3,14,90,611,4182,28658,196419,1346270,9227466,63245987,433494438,
%T A081005 2971215074,20365011075,139583862446,956722026042,6557470319843,
%U A081005 44945570212854,308061521170130,2111485077978051,14472334024676222,99194853094755498,679891637638612259
%N A081005 a(n) = Fibonacci(4n+3) + 1, or Fibonacci(2n+1)*Lucas(2n+2).
%D A081005 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081005 Nathaniel Johnston, <a href="/A081005/b081005.txt">Table of n, a(n) for n = 0..500</a>
%H A081005 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081005 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081005 G.f.: (3-10*x+2*x^2)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012
%F A081005 Product_{n>=0} (1 + 1/a(n)) = 1 + 1/sqrt(5) = A344212. - _Amiram Eldar_, Nov 28 2024
%p A081005 with(combinat): for n from 0 to 30 do printf(`%d,`,fibonacci(4*n+3)+1) od: # _James Sellers_, Mar 03 2003
%t A081005 Fibonacci[4Range[0,30]+3]+1 (* or *) LinearRecurrence[{8,-8,1}, {3,14,90}, 30] (* _Harvey P. Dale_, Jan 02 2013 *)
%o A081005 (Magma) [Fibonacci(4*n+3)+1: n in [0..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o A081005 (PARI) vector(30, n, n--; fibonacci(4*n+3)+1) \\ _G. C. Greubel_, Jul 15 2019
%o A081005 (Sage) [fibonacci(4*n+3)+1 for n in (0..30)] # _G. C. Greubel_, Jul 15 2019
%o A081005 (GAP) List([0..30], n-> Fibonacci(4*n+3)+1); # _G. C. Greubel_, Jul 15 2019
%Y A081005 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A344212.
%K A081005 nonn,easy
%O A081005 0,1
%A A081005 _R. K. Guy_, Mar 01 2003
%E A081005 More terms from _James Sellers_, Mar 03 2003