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(1/8)*number of equilateral triangles that can be formed from the points of an (n+1)X(n+1)X(n+1) lattice cube.
8

%I #13 Jul 07 2023 14:57:48

%S 1,10,46,158,431,974,2022,3837,6777,11263,17947,27541,40835,58904,

%T 83081,114543,155232,206901,271573,351583,449833,569225,712847,884408,

%U 1088136,1328616,1610007,1937077,2315434,2750476,3250073,3820925,4469597

%N (1/8)*number of equilateral triangles that can be formed from the points of an (n+1)X(n+1)X(n+1) lattice cube.

%H Ray Chandler, <a href="/A103501/b103501.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = A102698(n)/8.

%Y Cf. all triangles in lattice cube A103426; special triangles in lattice cube: A103427, A103428, A103429, A103499, A103500; A103158 tetrahedra in lattice cube.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Feb 08 2005

%E a(32)-a(100) from _Ray Chandler_, Sep 15 2007