计算{0，1，2，.}中的所有等边三角形，n}^3
Counting all equilateral triangles in {0,1,2,...,n}^3
摘要：
我们描述了一个计算三维空间中所有等边三角形的过程，这些三角形的坐标只允许在集合$\{0,1,...,n\}$中。这个序列在这里用ET（n）表示，并且它在“The On-Line Encyclopedia of Sequences”中具有条目A102698。该过程是在Maple中实现的，其主要思想是基于\cite{eji}中的结果。使用此，我们计算了n=1时的ET（n）值。55、这里有。叙述了有关该序列的一些事实和说明。其中最主要的是$\ds \lim_{n\to \infty} \frac{\ln ET(n)}{\ln n+1}$的存在。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
