A121346 Conjectured lower bound for the number of spheres of radius 1 that can be packed in a sphere of radius n.

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

Offset

2,1

Comments

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

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. 1 2016), pp. 2023-2033.

David W. Cantrell, Packing many equal small spheres into a large sphere, post in newsgroup sci.math, May 29 2006.

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.

Formula

a(n) = floor(K*(1 - 2*d)/d^3 + 1/(2*d^2)), where d=1/n and K = Pi/(3*sqrt(2)).

Crossrefs

Cf. A084828 (Maximum number of spheres of radius one that can be packed in a sphere of radius n).

Sequence in context: A213898 A085041 A197642 * A106847 A092761 A296733

Adjacent sequences: A121343 A121344 A121345 * A121347 A121348 A121349

Keyword

nonn

Author

Hugo Pfoertner, Jul 22 2006

Status

approved