This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156229 #9 Feb 17 2019 08:52:16 %S A156229 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 A156229 23,24,25,26,27,29,29,29,30,30,32,33,34,35,35,35,37,38,38,39,41,41,42, %U A156229 43,43,45,45,45,45,47,49,50,51,51,52 %N A156229 Partial sums of A052343. %C A156229 a(n) = (Pi/4)*n + O(sqrt(n)). %H A156229 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 A156229 a(n) = sum_{k=1..r(n)} r(2n-k^2+k)-C(r(n),2) where r(n) = A000194(n+1). %t A156229 terms = 61; QP = QPochhammer; %t A156229 s = QP[q^2]^4/QP[q]^2 + O[q]^terms; %t A156229 Ceiling[CoefficientList[s, q]/2] // Accumulate (* _Jean-François Alcover_, Feb 17 2019 *) %Y A156229 Cf. A052343, A000194. %K A156229 nonn %O A156229 0,2 %A A156229 _Vladimir Shevelev_, Feb 06 2009