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Acta Math. Univ. Comenianae


Abstract. 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}. 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.

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