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

2,2

Comments

For polygons with an odd number of sides see A070911.

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.

Example

The first entry is 1 because the convex lattice quadrilateral of minimal area is a unit square. The minimal area hexagon has area 3.

Crossrefs

The even-indexed subsequence of A070911. See also A063984.

Sequence in context: A173247 A123386 A060999 * A333980 A316319 A368205

Adjacent sequences: A089184 A089185 A089186 * A089188 A089189 A089190

Keyword

nonn

Author

Jamie Simpson, Dec 07 2003

Extensions

a(22) onwards from Günter Rote, Sep 17 2023

Status

approved