Geodesic
Counting all equilateral triangles in {0, 1, ..., n } 3
Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1 
E. J. Ionascu. Counting all equilateral triangles in {0, 1, ..., n } 3. Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a10/
@article{AMUC_2008_77_1_a10,
     author = {E. J. Ionascu},
     title = {Counting all equilateral triangles in {0, 1, ..., n } 3},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2008},
     volume = {77},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a10/}
}
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We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n } 3 . This sequence is denoted here by ET ( n ) and it has the entry A102698 in "The On-Line Encyclopedia of Integer Sequences". The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the values ET ( n ) for n = 1 ... 55 extending previous calculations known for n £ 34. Some facts and conjectures about this sequence are stated. The main conjecture raised here is that lim n ® ¥ ((ln ET ( n )) / (ln n + 1)) exists.