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

16, 45, 120, 211, 403, 714, 1023, 1830, 2700, 3659, 6125, 8101, 11027, 17280, 21499, 28689, 43012, 52736, 68557, 97733, 117776, 152344, 209409, 248983, 319957, 420714, 497676, 641229, 813814, 957001, 1214030, 1525951, 1774058, 2228111, 2747973, 3184761

Offset: 1

Author

Hugo Pfoertner, Dec 04 2018

Keywords

• nonn

Examples

			a(1) = 16 because there are 16 equivalence classes of lattice polygons having exactly 1 interior lattice point. See Pfoertner link.
		

Links

• Justus Springer, Table of n, a(n) for n = 1..60
• Wouter Castryck, Moving Out the Edges of a Lattice Polygon, Discrete Comput. Geom., 47 (2012), p. 496-518, Column N in Table 1, p 512.
• R. J. Koelman, The number of moduli families of curves on toric surfaces, Dissertation (1991), Chapter 4.2.
• Hugo Pfoertner, Illustration of polygons of genus 1 representing the 16 equivalence classes, (2018).
• B. Poonen and F. Rodriguez-Villegas, Lattice polygons and the number 12, Am. Math. Mon. 107 (2000), no. 3, 238-250 (2000).
• Justus Springer, RationalPolygons.jl (Version 1.0.0) [Computer software], 2024.

Crossrefs

Cf. A063984, A070911, A322344, A322345, A322346, A322347, A322348, A322349, A322350.

Extensions

a(31) onwards from Justus Springer, Oct 25 2024