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A070911 a(n) is twice the least possible area enclosed by a convex lattice n-gon. 7
1, 2, 5, 6, 13, 14, 21, 28, 43, 48, 65, 80, 103, 118, 151, 174, 213, 242, 289, 328, 387, 420, 497 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

A convex lattice n-gon is a polygon whose n vertices are points on the integer lattice Z^2 and whose interior angles are strictly less than Pi.

Sequence continues 1, 2, 5, 6, 13, 14, 21, 28, [39-43], 48, 65, 80.

LINKS

Table of n, a(n) for n=3..25.

I. Barany and N. Tokushige, The minimum area of convex lattice n-gons, Combinatorica, 24 (No. 2, 2004), 171-185.

Tian-Xin Cai, On the minimum area of convex lattice polygons, Taiwanese Journal of Mathematics, Vol 1, No 4 (1997).

W. Castryck, Moving Out the Edges of a Lattice Polygon, Discrete Comput. Geom., 47 (2012), p. 496-518.

Steven R. Finch, Convex Lattice Polygons, December 18, 2003. [Cached copy, with permission of the author]

Hugo Pfoertner, Illustrations of optimal polygons for n <= 20, (2018).

S. Rabinowitz, O(n^3) bounds for the area of a convex lattice n-gon, Geombinatorics, vol.II, 4(1993), p. 85-88.

R. J. Simpson, Convex lattice polygons of minimum area, Bulletin of the Australian Math. Society, 42 (1990), p. 353-367.

FORMULA

a(n)/2 = A063984(n) + n/2 - 1. [Simpson]

See Barany & Norihide for asymptotics.

CROSSREFS

See A089187 for the even-indexed subsequence. See A063984 for further information.

Cf. A321693, A322029.

Sequence in context: A232603 A069480 A100613 * A276082 A113240 A098376

Adjacent sequences:  A070908 A070909 A070910 * A070912 A070913 A070914

KEYWORD

nice,more,nonn

AUTHOR

Pierre Bornsztein (pbornszt(AT)club-internet.fr), May 20 2002

EXTENSIONS

Additional comments from Steven Finch, Dec 06 2003

a(11)-a(20) from Hugo Pfoertner, Nov 26 2018

a(21)-a(25) from Hugo Pfoertner, Dec 02 2018

STATUS

approved

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Last modified June 5 03:12 EDT 2020. Contains 334828 sequences. (Running on oeis4.)