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%I #28 Jan 02 2024 08:52:07
%S 3,32,231,1595,10944,75023,514227,3524576,24157815,165580139,
%T 1134903168,7778742047,53316291171,365435296160,2504730781959,
%U 17167680177563,117669030460992,806515533049391,5527939700884755,37889062373143904
%N a(n) = Fibonacci(4n+1) - 2, or Fibonacci(2n+2)*Lucas(2n-1).
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H G. C. Greubel, <a href="/A081012/b081012.txt">Table of n, a(n) for n = 1..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) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F G.f.: x*(3+8*x-x^2)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 22 2012
%F a(n) = 7*a(n-1) - a(n-2) + 10, n>=3. - _R. J. Mathar_, Nov 07 2015
%p with(combinat) for n from 0 to 25 do printf(`%d,`,fibonacci(4*n+1)-2) od # _James A. Sellers_, Mar 03 2003
%t Fibonacci[4*Range[30]+1] -2 (* _G. C. Greubel_, Jul 14 2019 *)
%o (Magma) [Fibonacci(4*n+1)-2: n in [1..30]]; // _Vincenzo Librandi_, Apr 20 2011
%o (PARI) vector(30, n, fibonacci(4*n+1)-2) \\ _G. C. Greubel_, Jul 14 2019
%o (Sage) [fibonacci(4*n+1)-2 for n in (1..30)] # _G. C. Greubel_, Jul 14 2019
%o (GAP) List([1..30], n-> Fibonacci(4*n+1) -2); # _G. C. Greubel_, Jul 14 2019
%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K nonn,easy
%O 1,1
%A _R. K. Guy_, Mar 01 2003
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