A138473 - OEIS

%I #25 Sep 08 2022 08:45:33

%S 0,21,987,46368,2178309,102334155,4807526976,225851433717,

%T 10610209857723,498454011879264,23416728348467685,1100087778366101931,

%U 51680708854858323072,2427893228399975082453,114059301025943970552219,5358359254990966640871840

%N a(n) = Fibonacci(8*n).

%H Colin Barker, <a href="/A138473/b138473.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-1).

%F a(n) = Fibonacci(4*n)*Lucas(4*n) = 21*A049668(n).

%F G.f.: 21*x / ( 1-47*x+x^2 ). - _R. J. Mathar_, Sep 30 2013

%F From _Colin Barker_, Apr 06 2017: (Start)

%F a(n) = (47 + 21*sqrt(5))^(1-n)*(-2^n+(2207 + 987*sqrt(5))^n) / (105 + 47*sqrt(5)).

%F a(n) = 47*a(n-1) - a(n-2) for n > 1.

%F (End)

%t Fibonacci[8Range[0,20]] (* _Harvey P. Dale_, Jun 22 2013 *)

%o (MuPAD) numlib::fibonacci(8*n) $ n = 0..25;

%o (Sage) [fibonacci(8*n) for n in range(0, 15)] # _Zerinvary Lajos_, May 15 2009

%o (Magma) [Fibonacci(8*n): n in [0..100]]; // _Vincenzo Librandi_, Apr 17 2011

%o (PARI) concat(0, Vec(21*x / (1 - 47*x + x^2) + O(x^30))) \\ _Colin Barker_, Apr 06 2017

%Y Cf. A000032, A000045, A049668, A134498.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, May 09 2008