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 A081006 #30 Jul 02 2025 16:02:01
%S A081006 2,20,143,986,6764,46367,317810,2178308,14930351,102334154,701408732,
%T A081006 4807526975,32951280098,225851433716,1548008755919,10610209857722,
%U A081006 72723460248140,498454011879263,3416454622906706,23416728348467684,160500643816367087
%N A081006 a(n) = Fibonacci(4n) - 1, or Fibonacci(2n+1)*Lucas(2n-1).
%C A081006 Apart from the offset, the same as A003481. - _R. J. Mathar_, Sep 18 2008
%D A081006 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081006 Nathaniel Johnston, <a href="/A081006/b081006.txt">Table of n, a(n) for n = 1..500</a>
%H A081006 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081006 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081006 G.f.: x*(2+4*x-x^2)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012
%p A081006 with(combinat) for n from 0 to 30 do printf(`%d,`,fibonacci(4*n)-1) od # _James Sellers_, Mar 03 2003
%t A081006 Fibonacci[4*Range[30]]-1 (* or *) LinearRecurrence[{8,-8,1}, {2,20,143}, 30] (* _Harvey P. Dale_, Mar 19 2018 *)
%o A081006 (Magma) [Fibonacci(4*n)-1: n in [1..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o A081006 (PARI) vector(30, n, fibonacci(4*n)-1) \\ _G. C. Greubel_, Jul 15 2019
%o A081006 (Sage) [fibonacci(4*n)-1 for n in (1..30)] # _G. C. Greubel_, Jul 15 2019
%o A081006 (GAP) List([1..30], n-> Fibonacci(4*n)-1); # _G. C. Greubel_, Jul 15 2019
%Y A081006 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K A081006 nonn,easy
%O A081006 1,1
%A A081006 _R. K. Guy_, Mar 01 2003
%E A081006 More terms from _James Sellers_, Mar 03 2003