#### Document Type

Article

#### Publication Date

2008

#### Publication Title

Acta Math. Univ. Comenianae

#### Abstract

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.

#### Recommended Citation

Ionascu, Eugen J., "Counting all equilateral triangles in {0, 1, …, n}³" (2008). *Faculty Bibliography*. 226.

http://csuepress.columbusstate.edu/bibliography_faculty/226