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%I #46 Oct 14 2023 23:43:05
%S 1,9,36,104,257,549,1058,1896,3199,5145,7926,11768,16967,23859,32846,
%T 44378,58977,77215,99684,126994,159963,199443,246304,301702,366729,
%U 442587,530508,631820,748121,880941,1031930,1202984,1395927,1612655,1855676,2127122,2429577
%N (1/2)*number of regular tetrahedra that can be formed using the points in an (n+1) X (n+1) X (n+1) lattice cube.
%D E. J. Ionascu, Regular tetrahedra whose vertices have integer coordinates. Acta Math. Univ. Comenian. (N.S.) 80 (2011), no. 2, 161-170; (Acta Mathematica Universitatis Comenianae) MR2835272 (2012h:11044).
%H Eugen J. Ionascu, <a href="/A103158/b103158.txt">Table of n, a(n) for n = 1..100</a>
%H Eugen J. Ionascu, <a href="http://dx.doi.org/10.1016/j.jnt.2009.01.003">A characterization of regular tetrahedra in Z^3</a>, Journal of Number Theory, Volume 129, Issue 5, May 2009, pp. 1066-1074.
%H Eugen J. Ionascu, <a href="http://arxiv.org/abs/0912.1062">Counting all regular tetrahedra in {0,1,...,n}^3</a>, arXiv:0912.1062 [math.NT], 2009.
%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, pp. 138-145.
%H Eugen J. Ionascu, <a href="https://www.emis.de/journals/AMUC/_vol-80/_no_2/_ionascu/ionascu.html">Regular tetrahedra whose vertices have integer coordinates</a>, Acta Mathematica Universitatis Comenianae, Vol. LXXX, 2 (2011) pp. 161-170.
%H Eugen J. Ionascu and R. A. Obando, <a href="http://www.emis.de/journals/INTEGERS/papers/a9self/a9self.Abstract.html">Cubes in {0,1,...,N}^3</a>, INTEGERS, 12A (2012), #A9. - From _N. J. A. Sloane_, Feb 05 2013
%e a(1)=1 because there are 2 ways to form a regular tetrahedron using vertices of the unit cube: Either [(0,0,0),(0,1,1),(1,0,1),(1,1,0)] or [(1,1,1),(1,0,0),(0,1,0),(0,0,1)].
%Y Cf. triangles in lattice cube: A103426, A103427, A103428, A103429, A103499, A103500; A096315 n+1 equidistant points in Z^n.
%Y Cf. A098928.
%K nonn
%O 1,2
%A _Hugo Pfoertner_, Feb 08 2005
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