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

3,2

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.

Sequence in context: A137950 A330100 A330099 * A364653 A046413 A353969

Adjacent sequences: A377242 A377243 A377244 * A377246 A377247 A377248

Keyword

nonn

Author

Justus Springer, Oct 21 2024

Status

approved