A089187 a(n) is the minimal area of a convex lattice polygon with 2n sides.
1, 3, 7, 14, 24, 40, 59, 87, 121, 164, 210, 274, 345, 430, 523, 632, 749, 890, 1039, 1222, 1412, 1620, 1838, 2088, 2357, 2651, 2953, 3278, 3612, 4020, 4439, 4902, 5387, 5898, 6418, 6974, 7557, 8182, 8835, 9512, 10218, 10984, 11759, 12635, 13525, 14448, 15399, 16415, 17473, 18570
Offset: 2
Keywords
Examples
The first entry is 1 because the convex lattice quadrilateral of minimal area is a unit square. The minimal area hexagon has area 3.
Links
- Günter Rote, Table of n, a(n) for n = 2..100
- Charles J. Colbourn and R. J. Simpson, A note on bounds on the minimum area of convex lattice polygons, Bull. Austral. Math. Soc., 45[1992], 237-240.
- Stanley Rabinowitz, Convex Lattice Polygons, Ph.D. Dissertation (Polytechnic University, Brooklyn, New York, 1986).
- Günter Rote, a(n), together with coordinates of some smallest 2n-gon, for n=2..100, (2023).
- Günter Rote, Python program for this sequence, and for A070911, (2023).
- R. J. Simpson, Convex lattice polygons of minimum area, Bull. Austral. Math. Soc., 42[1990], 353-367.
Extensions
a(22) onwards from Günter Rote, Sep 17 2023
Comments