A379894 -id:A379894 - cp's OEIS frontend

A379887 Number of rational polygons with denominator at most n having exactly one lattice point in their interior, up to equivalence.

16, 5145, 924042, 101267212, 8544548186

Offset: 1

Justus Springer, Jan 05 2025

A379894 counts the polygons with the extra condition that the vertices are primitive. Both are in Classification 5.6 of the article by Bohnert and Springer.

An algorithm to compute a(n) was given by Timo Hummel in his dissertation. His final number for n = 3 (given in Theorem 12.1) was however slightly off.

			For n = 1, there are 16 lattice polygons with exactly one interior lattice point, which are the 16 reflexive lattice polygons.

Martin Bohnert and Justus Springer, Classifying rational polygons with small denominator and few interior lattice points, arXiv:2410.17244 [math.CO], 2024.
Martin Bohnert and Justus Springer, Rational polygons with exactly one interior lattice point [Data set]. Zenodo.
Daniel Hättig, Jürgen Hausen, and Justus Springer, Classifying log del Pezzo surfaces with torus action, arXiv:2302.03095 [math.AG], 2023.
Daniel Hättig, Lattice Polygons and Surfaces with Torus Action, Dissertation (2023).
Timo Hummel, Automorphisms of rational projective K*-surfaces, Dissertation (2021).
Justus Springer, RationalPolygons.jl (Version 1.1.0) [Computer software], 2024.

Cf. A379894, A322343, A145581, A371917.

cp's OEIS Frontend

A379887 Number of rational polygons with denominator at most n having exactly one lattice point in their interior, up to equivalence.

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