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A121346
Conjectured lower bound for the number of spheres of radius 1 that can be packed in a sphere of radius n.
4
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
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jul 22 2006
STATUS
approved