%I #34 Jan 02 2024 08:52:24
%S 5,52,374,2581,17708,121390,832037,5702884,39088166,267914293,
%T 1836311900,12586269022,86267571269,591286729876,4052739537878,
%U 27777890035285,190392490709132,1304969544928654,8944394323791461
%N a(n) = Fibonacci(4n+2) - 3.
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F G.f.: x*(2*x^2-12*x-5)/((x-1)*(x^2-7*x+1)). - _Colin Barker_, Jun 22 2012
%F a(n) = Fibonacci(2*n+3)*Lucas(2*n-1). - _Ehren Metcalfe_, Apr 21 2019
%p with(combinat): for n from 1 to 40 do printf(`%d,`,fibonacci(4*n+2)-3) od: # _James A. Sellers_, Mar 05 2003
%t Array[Fibonacci[4 # + 2] - 3 &, 19] (* _Michael De Vlieger_, Apr 21 2019 *)
%o (Magma) [Fibonacci(4*n+2)-3: n in [1..50]]; // _Vincenzo Librandi_, Apr 20 2011
%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K nonn,easy
%O 1,1
%A _R. K. Guy_, Mar 04 2003
%E More terms from _James A. Sellers_, Mar 05 2003