Counting all regular tetrahedra in 0,1,...,n³

2009/12/05 by Eugen J. Ionaşcu, Eugen J. Ionascu, Ionascu, Eugen J.
Engineering · Mathematics · #11D09 #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11D09

paper · pdf · doi:10.48550/arxiv.0912.1062

21 pages, 6 figures, preprint

arxiv created 2009/12/05 · openalex publication_date 2009/12/05 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we describe a procedure of calculating the number all regular tetrahedra that have coordinates in the set 0,1,...,n. We develop a few results that may help in finding good estimates for this sequence which is twice A103158 in the Online Encyclopedia of Integer Sequences.

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