A377245 Number of equivalence classes of convex lattice polygons containing n lattice points, restricting the count to those polygons that are interior to another polygon.

1, 3, 4, 5, 7, 11, 16, 21, 25, 37, 46, 60, 69, 95, 110, 146, 179, 218, 258, 328, 378, 480, 557, 680, 792, 965, 1090, 1320, 1549, 1814, 2091, 2487, 2839, 3360, 3809, 4406, 5062, 5893, 6594, 7642, 8705, 9955, 11254, 12852, 14395, 16556, 18588, 20894, 23535

Offset: 3

Author

Justus Springer, Oct 21 2024

Keywords

• nonn

Comments

See Castryck article for an explanation how to check if a polygon is interior to another polygon by application of theorem 5 (Koelman 1991).

The polygons up to 112 lattice points can be downloaded from the zenodo dataset linked below.

Links

• Justus Springer, Table of n, a(n) for n = 3..112
• Wouter Castryck, Moving Out the Edges of a Lattice Polygon, Discrete Comput. Geom., 47 (2012), p. 496-518.
• R. J. Koelman, The number of moduli families of curves on toric surfaces, Dissertation (1991), Chapter 4.4.
• Justus Springer, RationalPolygons.jl (Version 1.0.0) [Computer software], 2024.
• Justus Springer and Martin Bohnert, Lattice polygons with at most 70 lattice points (1.1.0) [Data set], 2024.

Crossrefs

Cf. A371917, A322343, A322344, A187015.