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A136515 Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter 2n+1. 3
0, 2, 6, 12, 26, 38, 56, 74, 96, 128, 154, 188, 220, 262, 304, 344, 398, 452, 506, 562, 616, 686, 754, 824, 894, 976, 1056, 1134, 1224, 1308, 1406, 1500, 1592, 1694, 1804, 1914, 2026, 2136, 2258, 2374, 2504, 2626, 2756, 2892, 3022, 3164, 3300, 3450, 3600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of unit square lattice cells inside two adjacent quadrants of origin centered circle of radius n+1/2 As n -> infinity, lim a(n)/(n^2) -> pi/8

LINKS

Table of n, a(n) for n=0..48.

FORMULA

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

EXAMPLE

a(2) = 6 because a circle centered at the origin and of radius 2.5 encloses (-2,1),(-1,1),(-1,2),(2,1),(1,1),(1,2) in the upper half plane

MATHEMATICA

Table[2*Sum[Floor[Sqrt[(n + 1/2)^2 - k^2]], {k, 1, n}], {n, 0, 100}]

CROSSREFS

Cf. a(n) = 2 * A136484 = 1/2 * A136486 odd terms of A136513.

Sequence in context: A214663 A151385 A034875 * A141347 A246584 A054454

Adjacent sequences:  A136512 A136513 A136514 * A136516 A136517 A136518

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified March 28 05:07 EDT 2017. Contains 284182 sequences.