A084828
Maximum number of spheres of radius one that can be packed in a sphere of radius n.
Original entry on oeis.org
1, 2, 13, 32, 68
Offset: 1
- Sen Bai, X. Bai, X. Che, and X. Wei, Maximal Independent Sets in Heterogeneous Wireless Ad Hoc Networks, IEEE Transactions on Mobile Computing (Volume: 15, Issue: 8, Aug 01 2016), pp. 2023-2033.
- Dave Boll, Optimal Packing of Circles and Spheres.
- Sunil K. Chebolu, Packing Moons Inside the Earth, arXiv:2006.00603 [physics.pop-ph], 2020.
- WenQi Huang and Liang Yu, A Quasi Physical Method for the Equal Sphere Packing Problem, in 2011 IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications.
- WenQi Huang and Liang Yu, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, arXiv preprint arXiv:1202.4149 [cs.DM], 2012. - From _N. J. A. Sloane_, Jun 14 2012
- Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
- Hugo Pfoertner, Densest Packing of Spheres in a Sphere. Java visualization.
- Eckhard Specht, The best known packings of equal spheres in a sphere.
- Yu Liang, Coordinates of sphere centers of 68 spheres of radius 0.20000222, fitting into a container of radius 1. Private communication, Aug 22 2011.
a(5) corrected, based on private communication from Yu Liang, by
Hugo Pfoertner, Aug 24 2011
A084829
Best packing of m>1 equal spheres in a sphere setting a new density record.
Original entry on oeis.org
2, 3, 4, 6, 8, 9, 11, 12, 18, 21, 25, 30, 31, 32, 33, 34, 35, 36, 38, 49, 51, 53, 56, 59, 60, 61
Offset: 1
- Dave Boll, Optimal Packing of Circles and Spheres.
- WenQi Huang and Liang Yu, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, arXiv:1202.4149 [cs.DM], 2012.
- Eckard Specht, The best known packings of equal spheres in a sphere, July 2023.
- Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
- Hugo Pfoertner, Densest Packings of n Equal Spheres in a Sphere of Radius 1 Largest Possible Radii.
- Eric Weisstein's World of Mathematics, Sphere Packing.
- Jianrong Zhou, Shuo Ren, Kun He, Yanli Liu, and Chu-Min Li, An Efficient Solution Space Exploring and Descent Method for Packing Equal Spheres in a Sphere, arXiv:2305.10023 [cs.CG], 2023.
Inserted missing term 30, added comment with conjectured next terms and updated links by
Hugo Pfoertner, Jun 24 2011
A342559
Number of equal spheres setting a new density record in relation to the volume of the spherical layer that is occupied by the spheres when arranged touching the surface of a container sphere according to the criterion of maximizing their minimum mutual distance.
Original entry on oeis.org
2, 3, 4, 6, 8, 9, 10, 11, 12, 20, 24, 32, 38, 42, 44, 48
Offset: 1
a(n) Volume fraction in layer (rounded)
2 0.25000
3 0.30000
4 0.36364
6 0.42857
8 0.43853
9 0.45000
10 0.45152
11 0.46397
12 0.50615
20 0.51162
24 0.52941
32 0.53205
38 0.53373
42 0.53439
44 0.54286
48 0.54993
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