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A103609 Fibonacci numbers repeated (cf. A000045). 22
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, 233, 233, 377, 377, 610, 610, 987, 987, 1597, 1597, 2584, 2584, 4181, 4181, 6765, 6765, 10946, 10946, 17711, 17711, 28657, 28657, 46368, 46368, 75025, 75025, 121393 (list; graph; refs; listen; history; text; internal format)
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. BrĂ³d, 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) x='x+O('x^50); Vec(x^2*(1+x)/(1-x^2-x^4)) \\ G. C. Greubel, May 01 2017

CROSSREFS

Partial sums: A094707. - R. J. Mathar, Sep 27 2008

Cf. A214927.

Sequence in context: A090492 A325768 A239949 * A237800 A232697 A129526

Adjacent sequences:  A103606 A103607 A103608 * A103610 A103611 A103612

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

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Last modified August 4 15:50 EDT 2020. Contains 336202 sequences. (Running on oeis4.)