OFFSET
0,7
COMMENTS
The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - N. J. A. Sloane
The Gi2 sums, see A180662, of triangle A065941 equal the terms of this sequence without the two leading zeros. - Johannes W. Meijer, Aug 16 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, 2178 And All That, Fib. Quart., 52 (2014), 99-120.
I. Wloch, U. Bednarz, D. Bród, A Wloch and M. Wolowiec-Musial, On a new type of distance Fibonacci numbers, Discrete Applied Math., Volume 161, Issues 16-17, November 2013, Pages 2695-2701.
Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).
FORMULA
a(n) = a(n-2) + a(n-4).
G.f.: x^2*(1+x)/(1-x^2-x^4). - R. J. Mathar, Sep 27 2008
a(n) = A000045(floor(n/2)). - Johannes W. Meijer, Aug 16 2011
MAPLE
A103609 := proc(n): combinat[fibonacci](floor(n/2)) ; end proc: seq(A103609(n), n=0..52); # Johannes W. Meijer, Aug 16 2011
MATHEMATICA
a[0] = 0; a[1] = 0; a[2] = 1; a[3] = 1; a[n_Integer?Positive] := a[n] = a[n - 2] + a[n - 4]; aa = Table[a[n], {n, 0, 200}]
Join[{0, 0}, LinearRecurrence[{0, 1, 0, 1}, {1, 1, 1, 1}, 60]] (* Vincenzo Librandi, Jan 19 2016 *)
PROG
(PARI) a(n)=fibonacci(n\2) \\ Charles R Greathouse IV, Oct 07 2015
(PARI) my(x='x+O('x^50)); Vec(x^2*(1+x)/(1-x^2-x^4)) \\ G. C. Greubel, May 01 2017
(Magma) [Fibonacci(Floor(n/2)): n in [0..60]]; // G. C. Greubel, Oct 22 2024
(SageMath) [fibonacci(n//2) for n in range(61)] # G. C. Greubel, Oct 22 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Mar 24 2005
EXTENSIONS
Edited by N. J. A. Sloane, Dec 01 2006
Incorrect formula deleted by Johannes W. Meijer, Aug 16 2011
STATUS
approved