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 A081004 #33 Jul 02 2025 16:02:01
%S A081004 2,9,56,378,2585,17712,121394,832041,5702888,39088170,267914297,
%T A081004 1836311904,12586269026,86267571273,591286729880,4052739537882,
%U A081004 27777890035289,190392490709136,1304969544928658,8944394323791465,61305790721611592,420196140727489674
%N A081004 a(n) = Fibonacci(4n+2) + 1, or Fibonacci(2n+2)*Lucas(2n).
%D A081004 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081004 Nathaniel Johnston, <a href="/A081004/b081004.txt">Table of n, a(n) for n = 0..600</a>
%H A081004 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081004 a(n) = A033890(n)+1.
%F A081004 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081004 G.f.: (2-7*x)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012
%p A081004 with(combinat): for n from 0 to 30 do printf(`%d,`,fibonacci(4*n+2)+1) od: # _James Sellers_, Mar 03 2003
%t A081004 Table[Fibonacci[4n+2] +1, {n,0,30}] (* _Wesley Ivan Hurt_, Nov 20 2014 *)
%o A081004 (Magma) [Fibonacci(4*n+2)+1: n in [0..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o A081004 (PARI) vector(30, n, n--; fibonacci(4*n+2)+1) \\ _G. C. Greubel_, Jul 15 2019
%o A081004 (Sage) [fibonacci(4*n+2)+1 for n in (0..30)] # _G. C. Greubel_, Jul 15 2019
%o A081004 (GAP) List([0..30], n-> Fibonacci(4*n+2)+1); # _G. C. Greubel_, Jul 15 2019
%Y A081004 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A056854 (first differences).
%K A081004 nonn,easy
%O A081004 0,1
%A A081004 _R. K. Guy_, Mar 01 2003
%E A081004 More terms from _James Sellers_, Mar 03 2003