A138473 a(n) = Fibonacci(8*n).
0, 21, 987, 46368, 2178309, 102334155, 4807526976, 225851433717, 10610209857723, 498454011879264, 23416728348467685, 1100087778366101931, 51680708854858323072, 2427893228399975082453, 114059301025943970552219, 5358359254990966640871840
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (47,-1).
Programs
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Magma
[Fibonacci(8*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
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Mathematica
Fibonacci[8Range[0,20]] (* Harvey P. Dale, Jun 22 2013 *)
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MuPAD
numlib::fibonacci(8*n) $ n = 0..25;
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PARI
concat(0, Vec(21*x / (1 - 47*x + x^2) + O(x^30))) \\ Colin Barker, Apr 06 2017
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Sage
[fibonacci(8*n) for n in range(0, 15)] # Zerinvary Lajos, May 15 2009
Formula
a(n) = Fibonacci(4*n)*Lucas(4*n) = 21*A049668(n).
G.f.: 21*x / ( 1-47*x+x^2 ). - R. J. Mathar, Sep 30 2013
From Colin Barker, Apr 06 2017: (Start)
a(n) = (47 + 21*sqrt(5))^(1-n)*(-2^n+(2207 + 987*sqrt(5))^n) / (105 + 47*sqrt(5)).
a(n) = 47*a(n-1) - a(n-2) for n > 1.
(End)