Regular octahedra in {0, 1, ..., n}3
2012
scientific article
english
- diophantine equations
- regular octahedra
- Ehrhart polynomial
- sequence of integers
- primitive solutions
EN In this paper we describe a procedure for calculating the number of regular octahedra, RO(n), which 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 improve the method appeared in [12] which was used to find the number of regular tetrahedra with coordinates of their vertices in {0,1,..., n}. A new fact proved here helps increasing considerably the speed of all programs used before. The procedure is put together in a series of commands written for Maple and it is included in an earlier version of this paper in the matharxiv. Our technique allows us to find a series of cubic polynomials.
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