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A371917
Number of inequivalent convex lattice polygons containing n lattice points (including points on the boundary).
2
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
3,2
COMMENTS
A322343 counts the polygons by their number of interior lattice points, excluding points on the boundary.
LINKS
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.
EXAMPLE
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)}.
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Justus Springer, Apr 12 2024
STATUS
approved