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%I #27 Jul 04 2019 03:43:11
%S 0,1,2,3,5,8,12,19,30,47,75,120,192,309,498,803,1297,2096,3388,5479,
%T 8862,14335,23191,37520,60704,98217,158914,257123,416029,673144,
%U 1089164
%N Partial sums of ceiling(Fibonacci(n)/2).
%C Partial sums of A173173.
%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.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-2,0,1).
%F a(n) = round(Fibonacci(n+2)/2 + (n-1)/3).
%F a(n) = round(Fibonacci(n+2)/2 + n/3 - 1/2).
%F a(n) = floor(Fibonacci(n+2)/2 + n/3 - 1/6).
%F a(n) = ceiling(Fibonacci(n+2)/2 + n/3 - 1/2).
%F a(n) = a(n-3) + Fibonacci(n)+1, n > 2.
%F a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5.
%F G.f.: x*(x^3+x^2-1) / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ).
%e a(4) = 0 + 1 + 1 + 1 + 2 = 5.
%p seq(ceil(Fibonacci(n+2)/2+n/3-1/2),n=0..30)
%o (PARI) a(n)=(3*fibonacci(n+2)+2*n-1)\6 \\ _Charles R Greathouse IV_, Nov 02 2015
%Y Cf. A173173.
%K nonn,easy
%O 0,3
%A _Mircea Merca_, Jan 04 2011
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