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A084824
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Maximum number of spheres of diameter one that can be packed in a cube of volume n (i.e. with edge length n^(1/3)).
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4
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1, 1, 1, 2, 4, 4, 5, 8, 8, 8, 9, 9, 10, 11, 14, 14, 14, 15, 18, 18, 19, 19, 21, 21, 23, 24, 27, 27, 27, 27, 32, 32, 32, 33
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Higher sequence terms are only conjectures found by numerical experimentation.
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REFERENCES
| Goldberg, M., On the Densest Packing of Equal Spheres in a Cube. Math. Mag. 44, 199-208, 1971.
Schaer, J., On the Densest Packing of Spheres in a Cube. Can. Math. Bul. 9, 265-270, 1966.
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LINKS
| Dave Boll, Optimal Packing of Circles and Spheres
Thierry Gensane, Dense Packings of Equal Spheres in a Cube.The Electronic Journal of Combinatorics 11 (2004), #R33
Hugo Pfoertner, Best packing of equal spheres in a cube. Numerical results.
Hugo Pfoertner, Densest Packings of Equal Spheres in a Cube. Visualizations.
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EXAMPLE
| a(5)=4 because a cube of edge length 5^(1/3)=1.7099759 is large enough to contain 4 spheres arranged as a tetrahedron, which requires a minimum enclosing cube of edge length 1+sqrt(2)/2=1.70710678.
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CROSSREFS
| Cf. A084825, A084826, A084827, A084616.
Sequence in context: A111138 A035625 A132128 * A184615 A151969 A121528
Adjacent sequences: A084821 A084822 A084823 * A084825 A084826 A084827
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KEYWORD
| hard,more,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 12 2003
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EXTENSIONS
| Comment and dead links corrected by Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 23 2011
Corrected erroneous a(14) and extended to a(34) by Hugo Pfoertner, including results from Thierry Gensane (hugo(AT)pfoertner.org), Jun 23 2011
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