OFFSET
0,2
COMMENTS
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
George Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., Vol. 15, No. 3 (1977), pp. 233-236.
Index entries for linear recurrences with constant coefficients, signature (2,-5).
FORMULA
a(n) = 2*a(n-1) - 5*a(n-2); a(0)=0, a(1)=2. - T. D. Noe, Nov 09 2006
a(n) = - [M^n]_1,2, where M = [1, -2; 2, 1]. - Simone Severini, Apr 25 2007
From R. J. Mathar, Apr 06 2008: (Start)
O.g.f.: 2*x/(1 - 2*x + 5*x^2).
a(n) = 2*A045873(n). (End)
E.g.f.: exp(x)*sin(2*x). - Sergei N. Gladkovskii, Jul 22 2012
a(n)/A006495(n) = -tan(2*n*arctan(phi)), where phi is the golden ratio (A001622). - Amiram Eldar, Jan 13 2022
MATHEMATICA
LinearRecurrence[{2, -5}, {0, 2}, 30] (* Vincenzo Librandi, Dec 21 2011 *)
PROG
(Magma) I:=[0, 2]; [n le 2 select I[n] else 2*Self(n-1)-5*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Dec 21 2011
(PARI) a(n)=([1, -2; 2, 1]^n)[1, 2] \\ Charles R Greathouse IV, Dec 22 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Signs from Christian G. Bower, Nov 15 1998
Corrected by T. D. Noe, Nov 09 2006
More terms from R. J. Mathar, Apr 06 2008
STATUS
approved