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A179041 Partial sums of ceiling(Fibonacci(n)/3). 1
0, 1, 2, 3, 4, 6, 9, 14, 21, 33, 52, 82, 130, 208, 334, 538, 867, 1400, 2262, 3656, 5911, 9560, 15464, 25017, 40473, 65482, 105947, 171420, 277357, 448767, 726114, 1174871, 1900974, 3075834, 4976797, 8052619 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
FORMULA
a(n) = round(Fibonacci(n+2)/3 + 3*n/8 - 1/24).
a(n) = floor(Fibonacci(n+2)/3 + 3*n/8 + 1/4).
a(n) = ceiling(Fibonacci(n+2)/3 + 3*n/8 - 1/3).
a(n) = a(n-8) + Fibonacci(n-1) + Fibonacci(n-3) + 3, n > 7.
a(n) = 2*a(n-1) - a(n-3) + a(n-8) - 2*a(n-9) + a(n-11), n > 10.
G.f.: (x^9 + x^8 + x^4 + x^3 - x)/((x+1)*(x^2+1)*(x^2+x-1)*(x-1)^2*(x^4+1)).
a(n) = -1/16 + 3*n/8 - (-1)^n/16 + Fibonacci(n+2)/3 - A057077(n)/8 + (-1)^floor((n-1)/4)*A093148(n+1)/12. - R. J. Mathar, Jan 08 2011
EXAMPLE
a(9) = 0 + 1 + 1 + 1 + 1 + 2 + 3 + 5 + 7 + 12 = 33.
MAPLE
A179041 := proc(n) add( ceil(combinat[fibonacci](i)/3), i=0..n) ; end proc:
CROSSREFS
Sequence in context: A292800 A214041 A058355 * A099558 A018140 A256969
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved

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Last modified February 24 16:16 EST 2024. Contains 370307 sequences. (Running on oeis4.)