Counting all equilateral triangles in {0,1,2,...,n}^3
| dc.creator | Ionascu, Eugen J. | |
| dc.date | 2007-01-03 | |
| dc.date.accessioned | 2026-07-07T07:38:35Z | |
| dc.date.available | 2026-07-07T07:38:35Z | |
| dc.description | 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. | |
| dc.description | 12 pages, 1 figure, Maple code | |
| dc.identifier | https://arxiv.org/abs/math/0701111 | |
| dc.identifier | http://arxiv.org/abs/math/0701111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121136 | |
| dc.subject | General Mathematics | |
| dc.subject | Number Theory | |
| dc.subject | 11D09 | |
| dc.title | Counting all equilateral triangles in {0,1,2,...,n}^3 | |
| dc.type | text |