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Search: id:A136484
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| A136484 |
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Number of unit square lattice cells inside quadrant of origin centered circle of diameter 2n+1. |
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+0
4
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| 0, 1, 3, 6, 13, 19, 28, 37, 48, 64, 77, 94, 110, 131, 152, 172, 199, 226, 253, 281, 308, 343, 377, 412, 447, 488, 528, 567, 612, 654, 703, 750, 796, 847, 902, 957, 1013, 1068, 1129, 1187, 1252, 1313, 1378, 1446, 1511, 1582, 1650, 1725, 1800, 1877, 1955, 2034
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of unit square lattice cells inside quadrant of origin centered circle of radius n+1/2 As n -> infinity, lim a(n)/(n^2) -> pi/16
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FORMULA
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a(n) = Sum(floor(sqrt((n+1/2)^2 - k^2))), k = 1 ... n
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EXAMPLE
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a(2) = 3 because a circle of radius 2+1/2 in the first quadrant encloses (2,1),(1,1),(1,2)
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MATHEMATICA
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Table[Sum[Floor[Sqrt[(n + 1/2)^2 - k^2]], {k, 1, n}], {n, 0, 100}]
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CROSSREFS
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Cf. a(n) = 1/2 * A136515 = 1/4 * A136486 odd terms of A136483.
Sequence in context: A078382 A075651 A091277 this_sequence A137039 A137035 A137042
Adjacent sequences: A136481 A136482 A136483 this_sequence A136485 A136486 A136487
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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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