A084824 - OEIS

%I #21 Mar 23 2021 02:55:31

%S 1,1,1,2,4,4,5,8,8,8,9,9,10,11,14,14,14,15,18,18,19,19,21,21,23,24,27,

%T 27,27,27,32,32,32,33

%N Maximum number of spheres of diameter one that can be packed in a cube of volume n (i.e., with edge length n^(1/3)).

%C Higher sequence terms are only conjectures found by numerical experimentation.

%H Dave Boll, <a href="http://web.archive.org/web/20120714232416/https://home.comcast.net/~davejanelle/packing.html">Optimal Packing of Circles and Spheres</a>

%H Thierry Gensane, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r33">Dense Packings of Equal Spheres in a Cube</a>, The Electronic Journal of Combinatorics 11 (2004), #R33.

%H M. Goldberg, <a href="http://www.jstor.org/stable/2689076">On the Densest Packing of Equal Spheres in a Cube</a>, Math. Mag. 44, 199-208, 1971.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a084824.txt">Best packing of equal spheres in a cube. Numerical results.</a>

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sphere/incube/index.htm">Densest Packings of Equal Spheres in a Cube. Visualizations.</a>

%H J. Schaer, <a href="http://dx.doi.org/10.4153/CMB-1966-033-0">On the Densest Packing of Spheres in a Cube</a>, Can. Math. Bul. 9, 265-270, 1966.

%e a(5) = 4 because a cube of edge length 5^(1/3) = 1.7099759 is large enough to contain 4 spheres arranged as a tetrahedron, which requires a minimum enclosing cube of edge length 1+sqrt(2)/2 = 1.70710678.

%Y Cf. A084825, A084826, A084827, A084616.

%K hard,more,nonn

%O 1,4

%A _Hugo Pfoertner_, Jun 12 2003

%E Corrected erroneous a(14) and extended to a(34) by _Hugo Pfoertner_, including results from Thierry Gensane, Jun 23 2011