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Search: id:A136513
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| A136513 |
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Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter n. |
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+0
5
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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As n -> infinity, lim a(n)/(n^2) -> pi/8
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FORMULA
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a(n) = 2 * Sum(floor(sqrt((n/2)^2 - k^2))), k = 1 ... floor(n/2)
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EXAMPLE
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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
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MATHEMATICA
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Table[2*Sum[Floor[Sqrt[(n/2)^2 - k^2]], {k, 1, Floor[n/2]}], {n, 1, 100}]
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CROSSREFS
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Cf. Alternating merge of A136514 and A136515 a(n) = 2 * A136483 = 1/2 * A136485.
Sequence in context: A033748 A033736 A033760 this_sequence A054153 A000673 A129383
Adjacent sequences: A136510 A136511 A136512 this_sequence A136514 A136515 A136516
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KEYWORD
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easy,nonn
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AUTHOR
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Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
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