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A136515
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Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter 2n+1.
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3
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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; internal format)
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OFFSET
| 0,2
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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
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FORMULA
| a(n) = 2*Sum(floor(sqrt((n+1/2)^2 - k^2))), k = 1 ... n
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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
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MATHEMATICA
| Table[2*Sum[Floor[Sqrt[(n + 1/2)^2 - k^2]], {k, 1, n}], {n, 0, 100}]
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CROSSREFS
| Cf. a(n) = 2 * A136484 = 1/2 * A136486 odd terms of A136513.
Sequence in context: A099495 A151385 A034875 * A141347 A054454 A084170
Adjacent sequences: A136512 A136513 A136514 * A136516 A136517 A136518
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KEYWORD
| easy,nonn
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AUTHOR
| Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
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