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A178982
Partial sums of floor(Fibonacci(n)/2).
2
0, 0, 0, 1, 2, 4, 8, 14, 24, 41, 68, 112, 184, 300, 488, 793, 1286, 2084, 3376, 5466, 8848, 14321, 23176, 37504, 60688, 98200, 158896, 257105, 416010, 673124, 1089144, 1762278, 2851432, 4613721, 7465164, 12078896, 19544072, 31622980
OFFSET
0,5
COMMENTS
Partial sums of A004695.
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)/2 - (n+2)/3).
a(n) = round(Fibonacci(n+2)/2 - n/3 - 1/2).
a(n) = floor(Fibonacci(n+2)/2 - n/3 - 1/2).
a(n) = ceiling(Fibonacci(n+2)/2 - (n+1)/3 - 1/2).
a(n) = a(n-3) + Fibonacci(n) - 1, n > 3.
a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5.
G.f.: -x^3 / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ).
a(n) = (1/2) * (Fibonacci(n+2) + floor(n/3) - n - 1). - Ralf Stephan, Jan 19 2014
EXAMPLE
a(4) = 0 + 0 + 0 + 1 + 1 = 2.
MAPLE
seq(round(fibonacci(n+2)/2-(n+2)/3), n=0..40).
MATHEMATICA
f[n_] := Floor[Fibonacci@n/2]; Accumulate@ Array[f, 38, 0]
CROSSREFS
Sequence in context: A164168 A182747 A164406 * A164397 A164174 A164396
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 02 2011
STATUS
approved