Counting all regular octahedrons in {0,1,...,n}^3
Number Theory
2010-07-12 v1
Abstract
In this paper we describe a procedure for calculating the number of regular octahedrons that have vertices with coordinates in the set {0,1,...,n}. As a result, we introduce a new sequence in ``The Online Encyclopedia of Integer Sequences" (A178797) and list the first one hundred terms of it. We adapt the method appeared in [11] which was used to find the number of regular tetrahedra with coordinates of their vertices in {0,1,...,n}. The idea of this calculation is based on the theoretical results obtained in [14]. A new fact proved here helps increasing the speed of all the programs used before. The procedure is put together in a series of commands written for Maple.
Cite
@article{arxiv.1007.1655,
title = {Counting all regular octahedrons in {0,1,...,n}^3},
author = {Eugen J. Ionascu},
journal= {arXiv preprint arXiv:1007.1655},
year = {2010}
}
Comments
21 pages, 3 figures