A371917 Number of inequivalent convex lattice polygons containing n lattice points (including points on the boundary).

1, 3, 6, 13, 21, 41, 67, 111, 175, 286, 419, 643, 938, 1370, 1939, 2779, 3819, 5293, 7191, 9752, 12991, 17321, 22641, 29687, 38533, 49796, 63621, 81300, 102807, 129787, 162833, 203642, 252898, 313666, 386601, 475540, 582216, 710688, 863552, 1048176

Offset: 3

Author

Justus Springer, Apr 12 2024

Keywords

• nonn

Comments

A322343 counts the polygons by their number of interior lattice points, excluding points on the boundary.

Examples

			For n = 3, the only polygon is the standard triangle with vertices (0,0), (1,0) and (0,1).
For n = 4, a(4) = 3 and the three polygons have vertex sets {(1,0),(0,1),(-1,-1)}, {(0,0),(2,0),(0,1)} and {(0,0),(1,0),(0,1),(1,1)}.
		

Links

• Justus Springer, Table of n, a(n) for n = 3..112
• Martin Bohnert and Justus Springer, Classifying rational polygons with small denominator and few interior lattice points, arXiv:2410.17244 [math.CO], 2024. See p. 20.
• 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 M. Bohnert, Lattice polygons with at most 70 lattice points (1.0.0) [Data set], 2024.

Crossrefs

Cf. A187015, A322343, A322344.