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Search: id:A136486
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| A136486 |
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Number of unit square lattice cells enclosed by origin centered circle of diameter 2n+1. |
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+0
3
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| 0, 4, 12, 24, 52, 76, 112, 148, 192, 256, 308, 376, 440, 524, 608, 688, 796, 904, 1012, 1124, 1232, 1372, 1508, 1648, 1788, 1952, 2112, 2268, 2448, 2616, 2812, 3000, 3184, 3388, 3608, 3828, 4052, 4272, 4516, 4748, 5008, 5252, 5512, 5784, 6044, 6328, 6600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the number of complete squares that fit inside the circle with radius n+1/2, drawn on squared paper As n -> infinity, lim a(n)/(n^2) -> pi/4
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FORMULA
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a(n) = 4*Sum(floor(sqrt((n+1/2)^2 - k^2))), k = 1 ... n
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EXAMPLE
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a(1) = 4 because a circle centered at the origin and of radius 1+1/2 encloses (-1,-1),(-1,1),(1,-1),(1,1)
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MATHEMATICA
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Table[4*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) = 4 * A136484 = 2 * A136515 odd terms of A136485.
Sequence in context: A102651 A102652 A037338 this_sequence A003203 A051193 A025543
Adjacent sequences: A136483 A136484 A136485 this_sequence A136487 A136488 A136489
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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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