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A103158
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(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.
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17
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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
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OFFSET
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1,2
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REFERENCES
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Ionascu, E. J., 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).
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LINKS
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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, Pages 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, Pages 138-145.
Eugen J. Ionascu, Regular tetrahedra whose vertices have integer coordinates, Acta Mathematica Universitatis Comenianae , Vol. LXXX, 2 (2011) p. 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
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EXAMPLE
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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)].
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner, Feb 08 2005
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STATUS
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approved
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