2010/07/09 by Eugen J. Ionaşcu, Eugen J. Ionascu, Ionascu, Eugen J.
Computer Science · Mathematics · #11D09 #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11D09
paper · pdf · doi:10.48550/arxiv.1007.1655
21 pages, 3 figures
arxiv created 2010/07/09 · openalex publication_date 2010/07/09 · arxiv updated 2010/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.