A138473 a(n) = Fibonacci(8*n).

0, 21, 987, 46368, 2178309, 102334155, 4807526976, 225851433717, 10610209857723, 498454011879264, 23416728348467685, 1100087778366101931, 51680708854858323072, 2427893228399975082453, 114059301025943970552219, 5358359254990966640871840

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (47,-1).

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)

Mathematica

Fibonacci[8Range[0, 20]] (* Harvey P. Dale, Jun 22 2013 *)

Prog

(MuPAD) numlib::fibonacci(8*n) $ n = 0..25;
(Sage) [fibonacci(8*n) for n in range(0, 15)] # Zerinvary Lajos, May 15 2009
(Magma) [Fibonacci(8*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
(PARI) concat(0, Vec(21*x / (1 - 47*x + x^2) + O(x^30))) \\ Colin Barker, Apr 06 2017

Crossrefs

Cf. A000032, A000045, A049668, A134498.

Sequence in context: A220384 A184133 A004704 * A273281 A186392 A360505

Adjacent sequences: A138470 A138471 A138472 * A138474 A138475 A138476

Keyword

nonn,easy

Author

Zerinvary Lajos, May 09 2008

Status

approved