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

%I A379887 #16 Jan 05 2025 11:01:55
%S A379887 16,5145,924042,101267212,8544548186
%N A379887 Number of rational polygons with denominator at most n having exactly one lattice point in their interior, up to equivalence.
%C A379887 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.
%C A379887 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.
%H A379887 Martin Bohnert and Justus Springer, <a href="https://arxiv.org/abs/2410.17244">Classifying rational polygons with small denominator and few interior lattice points</a>, arXiv:2410.17244 [math.CO], 2024.
%H A379887 Martin Bohnert and Justus Springer, <a href="https://doi.org/10.5281/zenodo.13839216">Rational polygons with exactly one interior lattice point</a> [Data set]. Zenodo.
%H A379887 Daniel Hättig, Jürgen Hausen, and Justus Springer, <a href="https://arxiv.org/abs/2302.03095">Classifying log del Pezzo surfaces with torus action</a>, arXiv:2302.03095 [math.AG], 2023.
%H A379887 Daniel Hättig, <a href="http://hdl.handle.net/10900/136648">Lattice Polygons and Surfaces with Torus Action</a>, Dissertation (2023).
%H A379887 Timo Hummel, <a href="http://hdl.handle.net/10900/112895">Automorphisms of rational projective K*-surfaces</a>, Dissertation (2021).
%H A379887 Justus Springer, <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl (Version 1.1.0) [Computer software]</a>, 2024.
%e A379887 For n = 1, there are 16 lattice polygons with exactly one interior lattice point, which are the 16 reflexive lattice polygons.
%Y A379887 Cf. A379894, A322343, A145581, A371917.
%K A379887 nonn,more
%O A379887 1,1
%A A379887 _Justus Springer_, Jan 05 2025