A004697 a(n) = floor(Fibonacci(n)/4).

0, 0, 0, 0, 0, 1, 2, 3, 5, 8, 13, 22, 36, 58, 94, 152, 246, 399, 646, 1045, 1691, 2736, 4427, 7164, 11592, 18756, 30348, 49104, 79452, 128557, 208010, 336567, 544577, 881144, 1425721, 2306866, 3732588, 6039454

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Partial sums of A079962. - Mircea Merca, Jan 04 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,1,0,-1).

Crossrefs

See A000045 for the Fibonacci numbers.

Cf. A079962.

Programs

Magma

[Floor(Fibonacci(n)/4): n in [0..40]]; // Vincenzo Librandi, Jul 09 2012

Maple

A004697 := proc(n) floor(combinat[fibonacci](n)/4) ; end proc:

Mathematica

CoefficientList[Series[x^5/((1-x)*(1-x-x^2)*(1+x^2+x^4)),{x,0,50}],x] (* Vincenzo Librandi, Jul 09 2012 *)
Floor[Fibonacci[Range[0,50]]/4] (* or *) LinearRecurrence[ {2,-1,1,-1,1,0,-1},{0,0,0,0,0,1,2},50] (* Harvey P. Dale, Dec 05 2012 *)

PARI

vector(50, n, n--; fibonacci(n)\4) \\ G. C. Greubel, Oct 09 2018

Formula

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

From Mircea Merca, Jan 04 2011: (Start)

a(n) = floor(Fibonacci(n)/4).

a(n) = ceiling(Fibonacci(n)/4-3/4).

a(n) = round(Fibonacci(n)/4-3/8).

a(n) = Sum_{k=1..n-2} round(Fibonacci(n)/4).

a(n) = a(n-6) + Fibonacci(n-3), n > 5. (End)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-7). - R. J. Mathar, Jan 08 2011

a(n) = (A000045(n) - A079343(n))/4. - R. J. Mathar, Jul 14 2012