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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.
17
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, 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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Feb 08 2005
STATUS
approved