A103158 (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.

1, 9, 36, 104, 257, 549, 1058, 1896, 3199, 5145, 7926, 11768, 16967, 23859, 32846, 44378, 58977, 77215, 99684, 126994, 159963, 199443, 246304, 301702, 366729, 442587, 530508, 631820, 748121, 880941, 1031930, 1202984, 1395927, 1612655, 1855676, 2127122, 2429577

Offset: 1

Author

Hugo Pfoertner, Feb 08 2005

Keywords

• nonn

Examples

			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)].
		

References

• 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).

Links

• Eugen J. Ionascu, Table of n, a(n) for n = 1..100
• Eugen J. Ionascu, A characterization of regular tetrahedra in Z^3, Journal of Number Theory, Volume 129, Issue 5, May 2009, pp. 1066-1074.
• Eugen J. Ionascu, Counting all regular tetrahedra in {0,1,...,n}^3, arXiv:0912.1062 [math.NT], 2009.
• Eugen J. Ionascu, Andrei Markov, Platonic solids in Z^3, Journal of Number Theory, Volume 131, Issue 1, January 2011, pp. 138-145.
• Eugen J. Ionascu, Regular tetrahedra whose vertices have integer coordinates, Acta Mathematica Universitatis Comenianae, Vol. LXXX, 2 (2011) pp. 161-170.
• Eugen J. Ionascu and R. A. Obando, Cubes in {0,1,...,N}^3, INTEGERS, 12A (2012), #A9. - From _N. J. A. Sloane_, Feb 05 2013

Crossrefs

Cf. triangles in lattice cube: A103426, A103427, A103428, A103429, A103499, A103500; A096315 n+1 equidistant points in Z^n.

Cf. A098928.