

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
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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. 20232033.
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



