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%I #17 Jul 04 2019 03:13:39
%S 0,1,2,3,4,6,9,14,21,33,52,82,130,208,334,538,867,1400,2262,3656,5911,
%T 9560,15464,25017,40473,65482,105947,171420,277357,448767,726114,
%U 1174871,1900974,3075834,4976797,8052619
%N Partial sums of ceiling(Fibonacci(n)/3).
%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)/3 + 3*n/8 - 1/24).
%F a(n) = floor(Fibonacci(n+2)/3 + 3*n/8 + 1/4).
%F a(n) = ceiling(Fibonacci(n+2)/3 + 3*n/8 - 1/3).
%F a(n) = a(n-8) + Fibonacci(n-1) + Fibonacci(n-3) + 3, n > 7.
%F a(n) = 2*a(n-1) - a(n-3) + a(n-8) - 2*a(n-9) + a(n-11), n > 10.
%F G.f.: (x^9 + x^8 + x^4 + x^3 - x)/((x+1)*(x^2+1)*(x^2+x-1)*(x-1)^2*(x^4+1)).
%F a(n) = -1/16 + 3*n/8 - (-1)^n/16 + Fibonacci(n+2)/3 - A057077(n)/8 + (-1)^floor((n-1)/4)*A093148(n+1)/12. - _R. J. Mathar_, Jan 08 2011
%e a(9) = 0 + 1 + 1 + 1 + 1 + 2 + 3 + 5 + 7 + 12 = 33.
%p A179041 := proc(n) add( ceil(combinat[fibonacci](i)/3),i=0..n) ; end proc:
%K nonn
%O 0,3
%A _Mircea Merca_, Jan 04 2011
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