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A136514 Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of radius n. 1
0, 2, 8, 16, 30, 44, 60, 82, 108, 138, 166, 196, 238, 278, 324, 366, 416, 468, 526, 588, 644, 714, 780, 848, 930, 1008, 1090, 1170, 1256, 1350, 1438, 1540, 1638, 1744, 1856, 1954, 2072, 2180, 2310, 2432, 2548, 2678, 2808, 2950, 3090, 3220, 3366, 3510, 3664 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As n -> infinity, lim a(n)/(n^2) -> pi/8

LINKS

Table of n, a(n) for n=1..49.

FORMULA

a(n) = 2 * Sum(floor(sqrt(n^2 - k^2))), k = 1 ... n-1

a(n) = 2*A001182(n). - R. J. Mathar, Jan 10 2008

EXAMPLE

a(2) = 2 because a circle centered at the origin and of radius 2 encloses (-1,1) and (1,1) in the upper half plane

MATHEMATICA

Table[2*Sum[Floor[Sqrt[n^2 - k^2]], {k, 1, n-1}], {n, 1, 100}]

CROSSREFS

Cf. a(n) = 2 * Sum(floor(sqrt(n^2 - k^2))), k = 1 ... n-1 even terms of A136513.

Sequence in context: A137882 A194643 A327329 * A077071 A187216 A210729

Adjacent sequences:  A136511 A136512 A136513 * A136515 A136516 A136517

KEYWORD

easy,nonn

AUTHOR

Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008

STATUS

approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)