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

0,2

Comments

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

Links

Table of n, a(n) for n=0..60.

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

Formula

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

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 *)

Crossrefs

Cf. A052343, A000194.

Sequence in context: A049448 A354547 A130044 * A340901 A082081 A008475

Adjacent sequences: A156226 A156227 A156228 * A156230 A156231 A156232

Keyword

nonn

Author

Vladimir Shevelev, Feb 06 2009

Status

approved