A156229 Partial sums of A052343.

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, 23, 24, 25, 26, 27, 29, 29, 29, 30, 30, 32, 33, 34, 35, 35, 35, 37, 38, 38, 39, 41, 41, 42, 43, 43, 45, 45, 45, 45, 47, 49, 50, 51, 51, 52

Offset: 0

Author

Vladimir Shevelev, Feb 06 2009

Keywords

• nonn

Comments

a(n) = (Pi/4)*n + O(sqrt(n)).

Links

• V. Shevelev, Binary additive problems: theorems of Landau and Hardy-Littlewood type, arXiv:0902.1046 [math.NT], 2009-2012.

Crossrefs

Cf. A052343, A000194.

Programs

Mathematica

terms = 61; QP = QPochhammer;
s = QP[q^2]^4/QP[q]^2 + O[q]^terms;
Ceiling[CoefficientList[s, q]/2] // Accumulate (* Jean-François Alcover, Feb 17 2019 *)

Formula

a(n) = sum_{k=1..r(n)} r(2n-k^2+k)-C(r(n),2) where r(n) = A000194(n+1).