%I #28 Mar 01 2024 06:23:25
%S 4,11,58,380,2587,17714,121396,832043,5702890,39088172,267914299,
%T 1836311906,12586269028,86267571275,591286729882,4052739537884,
%U 27777890035291,190392490709138,1304969544928660,8944394323791467
%N Fibonacci(4n+2)+3, or Fibonacci(2n-1)*Lucas(2n+3).
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H Paolo Xausa, <a href="/A081073/b081073.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
%F G.f.: -(2*x^2-21*x+4)/((x-1)*(x^2-7*x+1)). - _Colin Barker_, Jun 22 2012
%p with(combinat): for n from 0 to 40 do printf(`%d,`,fibonacci(4*n+2)+3) od: # _James A. Sellers_, Mar 05 2003
%t Fibonacci[4*Range[0, 30]+2]+3 (* _Paolo Xausa_, Mar 01 2024 *)
%o (Magma) [Fibonacci(4*n+2)+3: n in [0..50]]; // _Vincenzo Librandi_, Apr 20 2011
%o (PARI) Vec(-(2*x^2-21*x+4)/((x-1)*(x^2-7*x+1)) + O(x^30)) \\ _Michel Marcus_, Dec 23 2014
%Y Cf. A000045 (Fibonacci numbers).
%K nonn,easy
%O 0,1
%A _R. K. Guy_, Mar 04 2003
%E More terms from _James A. Sellers_, Mar 05 2003