A178982 - OEIS

%I #30 Jul 04 2019 03:39:04

%S 0,0,0,1,2,4,8,14,24,41,68,112,184,300,488,793,1286,2084,3376,5466,

%T 8848,14321,23176,37504,60688,98200,158896,257105,416010,673124,

%U 1089144,1762278,2851432,4613721,7465164,12078896,19544072,31622980

%N Partial sums of floor(Fibonacci(n)/2).

%C Partial sums of A004695.

%H Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

%F a(n) = round(Fibonacci(n+2)/2 - (n+2)/3).

%F a(n) = round(Fibonacci(n+2)/2 - n/3 - 1/2).

%F a(n) = floor(Fibonacci(n+2)/2 - n/3 - 1/2).

%F a(n) = ceiling(Fibonacci(n+2)/2 - (n+1)/3 - 1/2).

%F a(n) = a(n-3) + Fibonacci(n) - 1, n > 3.

%F a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5.

%F G.f.: -x^3 / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ).

%F a(n) = (1/2) * (Fibonacci(n+2) + floor(n/3) - n - 1). - _Ralf Stephan_, Jan 19 2014

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

%p seq(round(fibonacci(n+2)/2-(n+2)/3),n=0..40).

%t f[n_] := Floor[Fibonacci@n/2]; Accumulate@ Array[f, 38, 0]

%Y Cf. A004695, A164397.

%K nonn

%O 0,5

%A _Mircea Merca_, Jan 02 2011