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A121346
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Conjectured lower bound for the number of spheres of radius 1 that can be packed in a sphere of radius n.
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4
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2, 11, 31, 68, 124, 205, 316, 460, 642, 866, 1138, 1461, 1839, 2278, 2781, 3354, 4000, 4724, 5531, 6424, 7409, 8490, 9671, 10956, 12351, 13859, 15485, 17234, 19110, 21116, 23259, 25542, 27969, 30546, 33276, 36164, 39215, 42432, 45821, 49385
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OFFSET
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2,1
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COMMENTS
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The formula was given by David W. Cantrell in a thread "Packing many equal small spheres into a larger sphere" in the newsgroup sci.math on May 29 2006.
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LINKS
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FORMULA
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a(n) = floor(K*(1 - 2*d)/d^3 + 1/(2*d^2)), where d=1/n and K = Pi/(3*sqrt(2)).
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CROSSREFS
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Cf. A084828 (Maximum number of spheres of radius one that can be packed in a sphere of radius n).
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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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