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A156229 Partial sums of A052343. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A088468 A049448 A130044 * A082081 A008475 A222416

Adjacent sequences:  A156226 A156227 A156228 * A156230 A156231 A156232

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Feb 06 2009

STATUS

approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)