This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103609 #51 Jul 11 2025 11:27:39
%S A103609 0,0,1,1,1,1,2,2,3,3,5,5,8,8,13,13,21,21,34,34,55,55,89,89,144,144,
%T A103609 233,233,377,377,610,610,987,987,1597,1597,2584,2584,4181,4181,6765,
%U A103609 6765,10946,10946,17711,17711,28657,28657,46368,46368,75025,75025,121393
%N A103609 Fibonacci numbers repeated (cf. A000045).
%C A103609 The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - _N. J. A. Sloane_
%C A103609 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
%H A103609 G. C. Greubel, <a href="/A103609/b103609.txt">Table of n, a(n) for n = 0..1000</a>
%H A103609 N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, Fib. Quart., 52 (2014), 99-120.
%H A103609 N. J. A. Sloane, <a href="/A001232/a001232.pdf">2178 And All That</a> [Local copy]
%H A103609 I. Wloch, U. Bednarz, D. Bród, A Wloch and M. Wolowiec-Musial, <a href="http://dx.doi.org/10.1016/j.dam.2013.05.029">On a new type of distance Fibonacci numbers</a>, Discrete Applied Math., Volume 161, Issues 16-17, November 2013, Pages 2695-2701.
%H A103609 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1).
%F A103609 a(n) = a(n-2) + a(n-4).
%F A103609 G.f.: x^2*(1+x)/(1-x^2-x^4). - _R. J. Mathar_, Sep 27 2008
%F A103609 a(n) = A000045(floor(n/2)). - _Johannes W. Meijer_, Aug 16 2011
%p A103609 A103609 := proc(n): combinat[fibonacci](floor(n/2)) ; end proc: seq(A103609(n), n=0..52); # _Johannes W. Meijer_, Aug 16 2011
%t A103609 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}]
%t A103609 Join[{0, 0}, LinearRecurrence[{0, 1, 0, 1}, {1, 1, 1, 1}, 60]] (* _Vincenzo Librandi_, Jan 19 2016 *)
%t A103609 With[{fibs=Fibonacci[Range[0,30]]},Riffle[fibs,fibs]] (* _Harvey P. Dale_, Jul 11 2025 *)
%o A103609 (PARI) a(n)=fibonacci(n\2) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A103609 (PARI) my(x='x+O('x^50)); Vec(x^2*(1+x)/(1-x^2-x^4)) \\ _G. C. Greubel_, May 01 2017
%o A103609 (Magma) [Fibonacci(Floor(n/2)): n in [0..60]]; // _G. C. Greubel_, Oct 22 2024
%o A103609 (SageMath) [fibonacci(n//2) for n in range(61)] # _G. C. Greubel_, Oct 22 2024
%Y A103609 Partial sums: A094707.
%Y A103609 Cf. A000045, A065941, A180662, A214927.
%K A103609 nonn,easy
%O A103609 0,7
%A A103609 _Roger L. Bagula_, Mar 24 2005
%E A103609 Edited by _N. J. A. Sloane_, Dec 01 2006
%E A103609 Incorrect formula deleted by _Johannes W. Meijer_, Aug 16 2011