A104221 a(n) = Fibonacci(n) - (Fibonacci(n) mod 2).

0, 0, 0, 2, 2, 4, 8, 12, 20, 34, 54, 88, 144, 232, 376, 610, 986, 1596, 2584, 4180, 6764, 10946, 17710, 28656, 46368, 75024, 121392, 196418, 317810, 514228, 832040, 1346268, 2178308, 3524578, 5702886, 9227464, 14930352, 24157816, 39088168

Offset

0,4

Comments

Also the circumference of the (n-2)-Fibonacci cube graph for n > 4. - Eric W. Weisstein, Sep 03 2017

Links

Robert Israel, Table of n, a(n) for n = 0..4781

Eric Weisstein's World of Mathematics, Fibonacci Cube Graph.

Eric Weisstein's World of Mathematics, Graph Circumference.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,-1).

Formula

a(n) = 2*A004695(n). - R. J. Mathar, Jul 23 2010

G.f.: 2*x^3/((1-x)*(1+x+x^2)*(1-x-x^2)). - R. J. Mathar, Jul 23 2010

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5). - Eric W. Weisstein, Sep 03 2017

a(n) = Fibonacci(n) - A011655(n). - David A. Corneth, Mar 25 2018

a(n) = (1/3)*(-2 +3*Fibonacci(n) + 2*ChebyshevU(n, -1/2) + ChebyshevU(n-1, -1/2)). - G. C. Greubel, Jul 08 2022

Maple

f:= gfun:-rectoproc({a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5),
seq(a(i)=[0, 0, 0, 2, 2][i+1], i=0..4)}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Mar 25 2018

Mathematica

2*Floor[Fibonacci[Range[0, 50]]/2] (* Eric W. Weisstein, Sep 03 2017 *)
Table[2/3 (Cos[2n*Pi/3] -1) +Fibonacci[n], {n, 0, 50}] (* Eric W. Weisstein, Sep 03 2017 *)
Table[(I^n*LucasL[n, I] -2)/3 +Fibonacci[n], {n, 0, 50}] (* Eric W. Weisstein, Mar 25 2018 *)
LinearRecurrence[{1, 1, 1, -1, -1}, {0, 0, 0, 2, 2}, 51] (* Eric W. Weisstein, Sep 03 2017 *)
CoefficientList[Series[(2x^3)/(1-x-x^2-x^3+x^4+x^5), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 03 2017 *)

Prog

(PARI) a(n) = 2*(fibonacci(n)\2); \\ Altug Alkan, Mar 25 2018
(Magma) [2*Floor(Fibonacci(n)/2): n in [0..40]]; // G. C. Greubel, Jul 08 2022
(SageMath) [2*(fibonacci(n)//2) for n in (0..40)] # G. C. Greubel, Jul 08 2022

Crossrefs

Cf. A000045, A004695, A011655, A049347.

Sequence in context: A086700 A332004 A364669 * A078044 A348851 A329664

Adjacent sequences: A104218 A104219 A104220 * A104222 A104223 A104224

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 14 2005

Status

approved