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
Brian Hopkins and Aram Tangboonduangjit, Arndt and De Morgan compositions, Integers 26 (2026), Art. A64. See p. 8 (Prop. 2).
N. J. A. Sloane, 2178 And All That, Fib. Quart. 52 (2014), 99-120.
N. J. A. Sloane, 2178 And All That. [Local copy]
Iwona Włoch, Urszula Bednarz, Dorota Bród, Andrzej Włoch, and Małgorzata Wołowiec-Musiał, On a new type of distance Fibonacci numbers, Disc. Appl. Math. 161(16-17) (November 2013), 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}]
(* Alternative: *)
Join[{0, 0}, LinearRecurrence[{0, 1, 0, 1}, {1, 1, 1, 1}, 60]] (* Vincenzo Librandi, Jan 19 2016 *)
(* Alternative: *)
With[{fibs=Fibonacci[Range[0, 30]]}, Riffle[fibs, fibs]] (* Harvey P. Dale, Jul 11 2025 *)
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