cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A084825 Maximum number of spheres of diameter one that can be packed in a cube of edge length n.

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%I A084825 #27 Jul 09 2025 11:54:54
%S A084825 1,8,27,66
%N A084825 Maximum number of spheres of diameter one that can be packed in a cube of edge length n.
%C A084825 From an extrapolation of Dave Boll's numerical results a(4)~=66 and a(5)~=141 are estimated values for the next terms.
%C A084825 However, E. Specht's data suggest a(5)=135. - _Hugo Pfoertner_, Jul 08 2025
%H A084825 Dave Boll, <a href="https://web.archive.org/web/20100529173628/https://home.comcast.net/~davejanelle/packing.html">Optimal Packing of Circles and Spheres</a>
%H A084825 Hugo Pfoertner, <a href="https://www.randomwalk.de/sphere/incube/index.htm">Densest Packings of Equal Spheres in a Cube</a>
%H A084825 Hugo Pfoertner, <a href="https://www.youtube.com/watch?v=70lfRHMLQWE">How to pack 66 spheres of diameter 1 in 4 x 4 x 4 cubic box</a>, YouTube video by Talabfahrer, 2016.
%H A084825 Hugo Pfoertner, <a href="/A084825/a084825.pdf">Observed number N of spheres in best packing known versus edge length x of cube</a>, comparison against empirical lower limit N > 1.325*x^2*(x-1), (2025).
%H A084825 Eckard Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html">The best known packings of equal spheres in a cube (complete up to N = 1000)</a>, 2013.
%e A084825 a(3)=27 because there is no known better arrangement than the 3*3*3 cubic one that would allow packing more than 27 spheres into a cube of edge length 3.
%Y A084825 Cf. A084824, A084828, A084617.
%K A084825 hard,more,nonn
%O A084825 1,2
%A A084825 _Hugo Pfoertner_, Jun 12 2003
%E A084825 a(4) from _Hugo Pfoertner_, May 21 2011