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%I #31 Jan 02 2024 08:52:00
%S 1,12,88,609,4180,28656,196417,1346268,9227464,63245985,433494436,
%T 2971215072,20365011073,139583862444,956722026040,6557470319841,
%U 44945570212852,308061521170128,2111485077978049,14472334024676220,99194853094755496
%N a(n) = Fibonacci(4n+3) - 1, or Fibonacci(2n+2)*Lucas(2n+1).
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H Nathaniel Johnston, <a href="/A081009/b081009.txt">Table of n, a(n) for n = 0..500</a>
%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.: (1+4*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+3)-1) od # _James A. Sellers_, Mar 03 2003
%t Fibonacci[4*Range[0,30] +3] -1 (* _G. C. Greubel_, Jul 14 2019 *)
%t LinearRecurrence[{8,-8,1},{1,12,88},30] (* _Harvey P. Dale_, Sep 23 2019 *)
%o (Magma) [Fibonacci(4*n+3)-1: n in [0..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o (PARI) vector(30, n, n--; fibonacci(4*n+3)-1) \\ _G. C. Greubel_, Jul 14 2019
%o (Sage) [fibonacci(4*n+3)-1 for n in (0..30)] # _G. C. Greubel_, Jul 14 2019
%o (GAP) List([0..30], n-> Fibonacci(4*n+3)-1); # _G. C. Greubel_, Jul 14 2019
%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K nonn,easy
%O 0,2
%A _R. K. Guy_, Mar 01 2003
%E More terms from _James A. Sellers_, Mar 03 2003
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