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Number of regular octahedra that can be formed using the points in an (n+1)X(n+1)X(n+1) lattice cube.
2

%I #13 Jan 24 2016 02:49:56

%S 0,1,8,32,104,261,544,1000,1696,2759,4296,6434,9352,13243,18304,24774,

%T 32960,43223,55976,71752,90936,113973,141312,173436,210960,254587,

%U 305000,364406,432824,511421,600992,702556,817200,946131,1090392,1251238

%N Number of regular octahedra that can be formed using the points in an (n+1)X(n+1)X(n+1) lattice cube.

%H Eugen J. Ionascu, <a href="/A178797/b178797.txt">Table of n, a(n) for n = 1..100</a>

%H Eugen J. Ionascu, <a href="http://arXiv.org/abs/1007.1655">Counting all regular octahedra in {0,1,...,n}^3</a>, arXiv:1007.1655 [math.NT], 2010.

%H Eugen J. Ionascu, Andrei Markov, <a href="http://dx.doi.org/10.1016/j.jnt.2010.07.008">Platonic solids in Z^3</a>, Journal of Number Theory, Volume 131, Issue 1, January 2011, Pages 138-145.

%e a(2)=1 because there is 1 way to form a regular octahedron using points of a {0,1,2}^3 lattice cube.

%Y Cf. A102698, A103158, A098928.

%K nonn

%O 1,3

%A _Eugen J. Ionascu_, Jun 15 2010

%E Edited by _Ray Chandler_, Jul 27 2010