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A004697
a(n) = floor(Fibonacci(n)/4).
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
0,7
COMMENTS
Partial sums of A079962. - Mircea Merca, Jan 04 2011
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
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
See A000045 for the Fibonacci numbers.
Cf. A079962.
Sequence in context: A349840 A293639 A320356 * A245271 A206743 A186085
KEYWORD
nonn,easy
STATUS
approved