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A036693
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Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n.
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2
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1, 4, 8, 16, 20, 32, 32, 36, 48, 56, 64, 60, 64, 88, 84, 96, 88, 104, 108, 120, 128, 116, 144, 136, 140, 168, 160, 168, 164, 176, 192, 180, 208, 200, 216, 228, 200, 240, 220, 264, 248, 236, 264, 264, 288, 284, 264, 296, 292, 312
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n)/n ~ 2*Pi.
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EXAMPLE
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a(10^2) = 660, a(10^3) = 6392, a(10^4) = 62952, a(10^5) = 628520, a(10^6) = 6281404. - Reinhard Zumkeller, Jan 13 2002
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PROG
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(Magma)
[#[<x, y>: x in [-n..n], y in [-n..n]| n-1 lt r and r le n where r is Sqrt(x^2+ y^2)]: n in [0..50]]; // Marius A. Burtea, Feb 18 2020
(Sage)
if n == 0: return 1
Range = lambda n: ((i, j) for i in (-n..n) for j in (-n..n))
return sum(1 for (j, k) in Range(n) if (n-1)^2 < j^2 + k^2 <= n^2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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