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A204043
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Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n.
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2
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OFFSET
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1,2
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COMMENTS
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Called "circle" because drawing a circle on the complex plane centered at 0 with radius n encloses the integers (with the exception of 0) that will be considered in computing a(n).
All terms of this sequence are purely real numbers.
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LINKS
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EXAMPLE
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a(1) = 1 * i * -1 * -i = -1. (Note that numbers like -1 + i are ignored here).
a(5) = 5 * (4 + 3i) * (3 + 4i) * 5i * (-3 + 4i) * (-4 + 3i) * ... (Note that the absolute value of numbers like 4 + 3i is precisely 5).
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MATHEMATICA
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Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[#] <= n &], {n, 10}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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