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

Eugen J. Ionascu

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

综合数学 2007-05-23 v1 数论

作者: Eugen J. Ionascu

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.

引用

@article{arxiv.math/0701111,
  title  = {Counting all equilateral triangles in {0,1,2,...,n}^3},
  author = {Eugen J. Ionascu},
  journal= {arXiv preprint arXiv:math/0701111},
  year   = {2007}
}

备注

12 pages, 1 figure, Maple code

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

摘要

引用

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