Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #32 Jan 02 2024 08:51:44
%S 2,9,56,378,2585,17712,121394,832041,5702888,39088170,267914297,
%T 1836311904,12586269026,86267571273,591286729880,4052739537882,
%U 27777890035289,190392490709136,1304969544928658,8944394323791465,61305790721611592,420196140727489674
%N a(n) = Fibonacci(4n+2) + 1, or Fibonacci(2n+2)*Lucas(2n).
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H Nathaniel Johnston, <a href="/A081004/b081004.txt">Table of n, a(n) for n = 0..600</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F a(n) = A033890(n)+1.
%F a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F G.f.: (2-7*x)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012
%p with(combinat): for n from 0 to 30 do printf(`%d,`,fibonacci(4*n+2)+1) od: # _James A. Sellers_, Mar 03 2003
%t Table[Fibonacci[4n+2] +1, {n,0,30}] (* _Wesley Ivan Hurt_, Nov 20 2014 *)
%o (Magma) [Fibonacci(4*n+2)+1: n in [0..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o (PARI) vector(30, n, n--; fibonacci(4*n+2)+1) \\ _G. C. Greubel_, Jul 15 2019
%o (Sage) [fibonacci(4*n+2)+1 for n in (0..30)] # _G. C. Greubel_, Jul 15 2019
%o (GAP) List([0..30], n-> Fibonacci(4*n+2)+1); # _G. C. Greubel_, Jul 15 2019
%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A056854 (first differences).
%K nonn,easy
%O 0,1
%A _R. K. Guy_, Mar 01 2003
%E More terms from _James A. Sellers_, Mar 03 2003