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A136513 Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter n. 4
0, 0, 2, 2, 6, 8, 12, 16, 26, 30, 38, 44, 56, 60, 74, 82, 96, 108, 128, 138, 154, 166, 188, 196, 220, 238, 262, 278, 304, 324, 344, 366, 398, 416, 452, 468, 506, 526, 562, 588, 616, 644, 686, 714, 754, 780, 824, 848, 894, 930, 976, 1008, 1056, 1090, 1134, 1170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

EXAMPLE

a(3) = 2 because a circle centered at the origin and of radius 3/2 encloses (-1,1) and (1,1) in the upper half plane

MATHEMATICA

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

CROSSREFS

Cf. Alternating merge of A136514 and A136515 a(n) = 2 * A136483 = 1/2 * A136485.

Sequence in context: A320067 A248823 A284616 * A214932 A322132 A054153

Adjacent sequences:  A136510 A136511 A136512 * A136514 A136515 A136516

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified August 8 04:32 EDT 2020. Contains 336290 sequences. (Running on oeis4.)