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A204044
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Lozenge Gaussian integer factorial, product of all nonzero Gaussian integers a + bi for which |a| + |b| <= n.
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2
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-1, 64, -3240000, 530841600000000, -791432829997056000000000000, 24298387172648346846064803840000000000000000, -30208456145049398593072092383690495361024000000000000000000000000
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OFFSET
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1,2
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COMMENTS
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Called "lozenge" because the Gaussian integers considered here form up a lozenge or diamond in the complex plane.
All terms are purely real integers.
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LINKS
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FORMULA
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EXAMPLE
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a(2) = -2 * (-1 - i) * -1 * (-1 + i) * -2i * -i * i * 2i * (1 - i) * 1 * (1 + i) * 2 = 64. (Note that numbers like -2 + i are skipped over in the computation of a(2) because abs(-2) + abs(1) > 2).
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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[Re[#]] + Abs[Im[#]] <= n&], {n, 10}]
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PROG
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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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