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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

%I

%S 2,11,31,68,124,205,316,460,642,866,1138,1461,1839,2278,2781,3354,

%T 4000,4724,5531,6424,7409,8490,9671,10956,12351,13859,15485,17234,

%U 19110,21116,23259,25542,27969,30546,33276,36164,39215,42432,45821,49385

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

%C 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.

%H Hugo Pfoertner, <a href="/A121346/b121346.txt">Table of n, a(n) for n = 2..10000</a>

%H Sen Bai, X. Bai, X. Che, and X. Wei, <a href="https://doi.org/10.1109/TMC.2015.2508805">Maximal Independent Sets in Heterogeneous Wireless Ad Hoc Networks</a>, IEEE Transactions on Mobile Computing (Volume: 15, Issue: 8, Aug. 1 2016), pp. 2023-2033.

%H David W. Cantrell, <a href="https://groups.google.com/g/sci.math/c/Q9OMtGmXNbg/m/a_AnL8wYel8J">Packing many equal small spheres into a large sphere</a>, post in newsgroup sci.math, May 29 2006.

%H WenQi Huang and Liang Yu, <a href="https://doi.ieeecomputersociety.org/10.1109/TrustCom.2011.233">A Quasi Physical Method for the Equal Sphere Packing Problem</a>, in 2011 IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications.

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

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

%K nonn

%O 2,1

%A _Hugo Pfoertner_, Jul 22 2006

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Last modified July 26 22:10 EDT 2021. Contains 346300 sequences. (Running on oeis4.)