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

1,2

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

Example

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)].

Crossrefs

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

Cf. A098928.

Sequence in context: A114286 A098928 A139469 * A298442 A212104 A193007

Adjacent sequences: A103155 A103156 A103157 * A103159 A103160 A103161

Keyword

nonn

Author

Hugo Pfoertner, Feb 08 2005

Status

approved