A004698 a(n) = floor(Fibonacci(n)/5).

0, 0, 0, 0, 0, 1, 1, 2, 4, 6, 11, 17, 28, 46, 75, 122, 197, 319, 516, 836, 1353, 2189, 3542, 5731, 9273, 15005, 24278, 39283, 63562, 102845, 166408, 269253, 435661, 704915, 1140577, 1845493, 2986070, 4831563

Offset

0,8

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,2,1,-3,-1,3,0,-2,1,2,-1,-1).

Formula

G.f.: x^5*(1+x)*(1-x+x^3-x^5+x^7)/((1-x-x^2)*(1-x^5)*(1-x^2+x^4-x^6+x^8)).

a(n) = (A000045(n) - A082116(n))/5. - R. J. Mathar, Jul 14 2012

Maple

seq(floor(fibonacci(n)/5), n=0..40); # Muniru A Asiru, Oct 10 2018

Mathematica

CoefficientList[Series[(x^5(1+x)(1-x+x^3-x^5+x^7))/((1-x-x^2)(1-x^5)(1-x^2+x^4-x^6+x^8)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 09 2012 *)
LinearRecurrence[{1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1}, {0, 0, 0, 0, 0, 1, 1, 2, 4, 6, 11, 17, 28, 46, 75}, 40] (* Harvey P. Dale, Mar 14 2016 *)

Prog

(Magma) [Floor(Fibonacci(n)/5): n in [0..40]]; // Vincenzo Librandi, Jul 09 2012
(PARI) vector(50, n, n--; fibonacci(n)\5) \\ G. C. Greubel, Oct 09 2018

Crossrefs

Sequence in context: A210520 A018144 A115315 * A014217 A034297 A326495

Adjacent sequences: A004695 A004696 A004697 * A004699 A004700 A004701

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved