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Search: id:A136483
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| A136483 |
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Number of unit square lattice cells inside quadrant of origin-centered circle of diameter n. |
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+0
4
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| 0, 0, 1, 1, 3, 4, 6, 8, 13, 15, 19, 22, 28, 30, 37, 41, 48, 54, 64, 69, 77, 83, 94, 98, 110, 119, 131, 139, 152, 162, 172, 183, 199, 208, 226, 234, 253, 263, 281, 294, 308, 322, 343, 357, 377, 390, 412, 424, 447, 465, 488, 504, 528, 545, 567, 585, 612, 628, 654
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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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/2)^2 - k^2))), k = 1 ... floor(n/2)
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EXAMPLE
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a(5) = 3 because a circle of radius 5/2 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/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 A136484 and A001182 a(n) = 1/4 * A136485 = 1/2 * A136513.
Adjacent sequences: A136480 A136481 A136482 this_sequence A136484 A136485 A136486
Sequence in context: A145751 A063759 A139041 this_sequence A004713 A050475 A025073
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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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