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%I #9 Feb 17 2019 08:52:16
%S 1,2,3,4,5,5,7,8,8,9,10,11,12,13,13,14,16,16,17,17,18,20,21,21,22,23,
%T 23,24,25,26,27,29,29,29,30,30,32,33,34,35,35,35,37,38,38,39,41,41,42,
%U 43,43,45,45,45,45,47,49,50,51,51,52
%N Partial sums of A052343.
%C a(n) = (Pi/4)*n + O(sqrt(n)).
%H V. Shevelev, <a href="http://arXiv.org/abs/0902.1046">Binary additive problems: theorems of Landau and Hardy-Littlewood type</a>, arXiv:0902.1046 [math.NT], 2009-2012.
%F a(n) = sum_{k=1..r(n)} r(2n-k^2+k)-C(r(n),2) where r(n) = A000194(n+1).
%t terms = 61; QP = QPochhammer;
%t s = QP[q^2]^4/QP[q]^2 + O[q]^terms;
%t Ceiling[CoefficientList[s, q]/2] // Accumulate (* _Jean-François Alcover_, Feb 17 2019 *)
%Y Cf. A052343, A000194.
%K nonn
%O 0,2
%A _Vladimir Shevelev_, Feb 06 2009