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A322343 Number of equivalence classes of convex lattice polygons of genus n.

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%I A322343 #23 Oct 26 2024 10:43:43
%S A322343 16,45,120,211,403,714,1023,1830,2700,3659,6125,8101,11027,17280,
%T A322343 21499,28689,43012,52736,68557,97733,117776,152344,209409,248983,
%U A322343 319957,420714,497676,641229,813814,957001,1214030,1525951,1774058,2228111,2747973,3184761
%N A322343 Number of equivalence classes of convex lattice polygons of genus n.
%H A322343 Justus Springer, <a href="/A322343/b322343.txt">Table of n, a(n) for n = 1..60</a>
%H A322343 Wouter Castryck, <a href="http://dx.doi.org/10.1007/s00454-011-9376-2">Moving Out the Edges of a Lattice Polygon</a>, Discrete Comput. Geom., 47 (2012), p. 496-518, Column N in Table 1, p 512.
%H A322343 R. J. Koelman, <a href="https://hdl.handle.net/2066/113957">The number of moduli families of curves on toric surfaces</a>, Dissertation (1991), Chapter 4.2.
%H A322343 Hugo Pfoertner, <a href="/A322343/a322343.txt">Illustration of polygons of genus 1 representing the 16 equivalence classes,</a> (2018).
%H A322343 B. Poonen and F. Rodriguez-Villegas, <a href="http://www-math.mit.edu/~poonen/papers/lattice12.pdf">Lattice polygons and the number 12</a>, Am. Math. Mon. 107 (2000), no. 3, 238-250 (2000).
%H A322343 Justus Springer, <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl (Version 1.0.0) [Computer software]</a>, 2024.
%e A322343 a(1) = 16 because there are 16 equivalence classes of lattice polygons having exactly 1 interior lattice point. See Pfoertner link.
%Y A322343 Cf. A063984, A070911, A322344, A322345, A322346, A322347, A322348, A322349, A322350.
%K A322343 nonn
%O A322343 1,1
%A A322343 _Hugo Pfoertner_, Dec 04 2018
%E A322343 a(31) onwards from _Justus Springer_, Oct 25 2024