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A187015 The number of different classes of 2-dimensional convex lattice polytopes having volume n/2 up to unimodular equivalence.

%I A187015 #63 May 09 2025 10:30:28
%S A187015 1,2,3,7,6,13,13,27,26,44,43,83,81,122,136,208,215,317,341,490,542,
%T A187015 710,778,1073,1186,1519,1708,2178,2405,3042,3408,4247,4785,5782,6438,
%U A187015 7870,8833,10560,11857,14131,15733,18636,20773,24381,27353,31764,35284,41081,45791,52762
%N A187015 The number of different classes of 2-dimensional convex lattice polytopes having volume n/2 up to unimodular equivalence.
%C A187015 Lattice polytopes up to the equivalence relation used here are also called toric diagrams, see references below. - _Andrey Zabolotskiy_, May 10 2019
%C A187015 Liu & Zong give a(7) = 11, and others use their list, but their list lacks polygons No. 3 and 4 from Balletti's file 2-polytopes/v7.txt. - _Andrey Zabolotskiy_, Dec 28 2021
%H A187015 Günter Rote, <a href="/A187015/b187015.txt">Table of n, a(n) for n = 1..207</a>
%H A187015 Gabriele Balletti, <a href="https://github.com/gabrieleballetti/small-lattice-polytopes">Dataset of "small" lattice polytopes</a>. Beware that the vertices are not always listed in sorted order around the polygon boundary (clockwise or counterclockwise).
%H A187015 Gabriele Balletti, <a href="https://doi.org/10.1007/s00454-020-00187-y">Enumeration of lattice polytopes by their volume</a>, Discrete Comput. Geom., 65 (2021), 1087-1122; arXiv:<a href="https://arxiv.org/abs/1811.03357">1103.0103</a> [math.CO], 2018.
%H A187015 Sebastián Franco, Yang-Hui He, Chuang Sun and Yan Xiao, <a href="https://doi.org/10.1142/S0217751X17501421">A comprehensive survey of brane tilings</a>, Int. J. Mod. Phys. A, 32 (2017), 1750142, <a href="https://arxiv.org/abs/1702.03958">arXiv:1702.03958</a> [hep-th], 2017.
%H A187015 Heling Liu and Chuanming Zong, <a href="https://doi.org/10.1515/advgeom.2011.031">On the classification of convex lattice polytopes</a>, Adv. Geom., 11 (2011), 711-729, <a href="https://arxiv.org/abs/1103.0103">arXiv:1103.0103</a> [math.MG], 2011. See table at p. 8.
%H A187015 Günter Rote, <a href="/A187015/a187015_1.txt">Number of lattice polygons of area at most 103.5, classified by the number k of vertices, the number B of lattice points on edges, and the number I of interior lattice points</a>.
%H A187015 Yan Xiao, <a href="https://openaccess.city.ac.uk/id/eprint/22113">Quivers, Tilings and Branes</a>, City, University of London, 2018. See Tables 3.2-3.7.
%o A187015 (Python) # See the Python program for A366409.
%Y A187015 Cf. A126587, A003051 (triangles only), A322343, A366409.
%K A187015 nonn
%O A187015 1,2
%A A187015 _Jonathan Vos Post_, Mar 01 2011
%E A187015 a(8) from Yan Xiao added by _Andrey Zabolotskiy_, May 10 2019
%E A187015 Name edited, a(7) corrected, a(9)-a(50) added using Balletti's data by _Andrey Zabolotskiy_, Dec 28 2021