{
  "id": "1007.1655",
  "version": "v1",
  "published": "2010-07-09T19:46:45.000Z",
  "updated": "2010-07-09T19:46:45.000Z",
  "title": "Counting all regular octahedrons in {0,1,...,n}^3",
  "authors": [
    "Eugen J. Ionascu"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-09T19:46:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09"
    ],
    "keywords": [
      "regular octahedrons",
      "coordinates",
      "online encyclopedia",
      "integer sequences",
      "regular tetrahedra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.1655I"
    }
  }
}