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A179001
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Partial sums of floor(Fibonacci(n)/3).
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1
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0, 0, 0, 0, 1, 2, 4, 8, 15, 26, 44, 73, 121, 198, 323, 526, 855, 1387, 2248, 3641, 5896, 9544, 15447, 24999, 40455, 65463, 105927, 171399, 277336, 448745, 726091, 1174847, 1900950, 3075809, 4976771, 8052592, 13029376, 21081981, 34111370, 55193365, 89304750
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OFFSET
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0,6
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COMMENTS
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Partial sums of A004696.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..280
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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FORMULA
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a(n)=round(Fibonacci(n+2)/3-3*n/8-11/24).
a(n)=round(Fibonacci(n+2)/3-3*n/8-1/3).
a(n)=floor(Fibonacci(n+2)/3-3*n/8-1/6).
a(n)=ceil(Fibonacci(n+2)/3-3*n/8-3/4).
a(n)=a(n-8)+Fibonacci(n-1)+Fibonacci(n-3)-3, n>8.
a(n)=2*a(n-1)-a(n-3)+a(n-8)-2*a(n-9)+a(n-11), n>10.
G.f.: -x^4*(1+x^4+x^3) / ( (1+x)*(x^2+1)*(x^2+x-1)*(x^4+1)*(x-1)^2 ).
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EXAMPLE
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a(9)=0+0+0+0+1+1+2+4+7+11=26.
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MAPLE
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A179001 := proc(n) add( floor(combinat[fibonacci](i)/3), i=0..n) ; end proc:
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PROG
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(MAGMA) [Floor(Fibonacci(n+2)/3-3*n/8-1/6): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
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CROSSREFS
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Cf. A004696.
Sequence in context: A114226 A210063 A187154 * A222147 A003241 A182844
Adjacent sequences: A178998 A178999 A179000 * A179002 A179003 A179004
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KEYWORD
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nonn
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AUTHOR
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Mircea Merca, Jan 03 2011
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STATUS
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approved
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