Counting all equilateral triangles in {0,1,2,...,n}^3

Details Counting all equilateral triangles in {0,1,2,...,n}^3 Counting all equilateral triangles in {0,1,2,...,n}^3

2007-01-03

arxiv.org/abs/math/0701111v1

Mathematics

General Mathematics

12 pages, 1 figure, Maple code

Scientific paper

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 \cite{eji}. Using this we calculated the values ET(n) for n=1..55 which are included here. Some facts and conjectures about this sequence are stated. The main of them is that $\ds \lim_{n\to \infty} \frac{\ln ET(n)}{\ln n+1}$ exists.

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