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
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 02 2011
STATUS
approved