A178982 Partial sums of floor(Fibonacci(n)/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

Author

Mircea Merca, Jan 02 2011

Keywords

• nonn

Comments

Partial sums of A004695.

Examples

			a(4) = 0 + 0 + 0 + 1 + 1 = 2.
		

Links

• Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Crossrefs

Cf. A004695, A164397.

Programs

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]

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