OFFSET
0,7
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).
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
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 *)
PROG
(Magma) [Floor(Fibonacci(n)/4): n in [0..40]]; // Vincenzo Librandi, Jul 09 2012
(PARI) vector(50, n, n--; fibonacci(n)\4) \\ G. C. Greubel, Oct 09 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved