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

Offset

1,1

Links

Table of n, a(n) for n=1..30.

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).

Poonen, B., Rodriguez-Villegas, F., Lattice polygons and the number 12, Am. Math. Mon. 107 (2000), no. 3, 238-250 (2000).

Example

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

Crossrefs

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

Sequence in context: A359704 A051868 A209993 * A345754 A318093 A223029

Adjacent sequences: A322340 A322341 A322342 * A322344 A322345 A322346

Keyword

nonn,more,changed

Author

Hugo Pfoertner, Dec 04 2018

Status

approved