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A179006 Partial sums of floor(Fibonacci(n)/4). 1
0, 0, 0, 0, 0, 1, 3, 6, 11, 19, 32, 54, 90, 148, 242, 394, 640, 1039, 1685, 2730, 4421, 7157, 11584, 18748, 30340, 49096, 79444, 128548, 208000, 336557, 544567, 881134, 1425711, 2306855, 3732576, 6039442, 9772030, 15811484 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Partial sums of A004697.
LINKS
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) - a(n-7) + a(n-8).
a(n) = round(Fibonacci(n+2)/4 - n/3 - 3/8).
a(n) = round(Fibonacci(n+2)/4 - n/3 - 1/4).
a(n) = floor(Fibonacci(n+2)/4 - n/3 - 1/12).
a(n) = ceiling(Fibonacci(n+2)/4 - n/3 - 2/3).
a(n) = a(n-6) + Fibonacci(n-1) - 2, n > 6.
G.f.: -x^5/((x^2+x+1)*(x^2-x+1)*(x^2+x-1)*(x-1)^2).
EXAMPLE
a(7) = 0 + 0 + 0 + 0 + 0 + 1 + 2 + 3 = 6.
MAPLE
A179006 := proc(n) add( floor(combinat[fibonacci](i)/4), i=0..n) ; end proc:
MATHEMATICA
f[n_] := Floor[ Fibonacci@ n/4]; Accumulate@ Array[f, 38]
LinearRecurrence[{3, -3, 2, -2, 2, -1, -1, 1}, {0, 0, 0, 0, 0, 1, 3, 6}, 40] (* Harvey P. Dale, Jan 28 2020 *)
PROG
(PARI) a(n)={round(fibonacci(n+2)/4 - n/3 - 3/8)} \\ Andrew Howroyd, May 01 2020
CROSSREFS
Cf. A004697.
Sequence in context: A116557 A001911 A020957 * A281573 A262987 A191696
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 03 2011
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)