

A070911


a(n) is twice the least possible area enclosed by a convex lattice ngon.


7



1, 2, 5, 6, 13, 14, 21, 28, 43, 48, 65, 80, 103, 118, 151, 174, 213, 242, 289, 328, 387, 420, 497
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OFFSET

3,2


COMMENTS

A convex lattice ngon 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, [3943], 48, 65, 80.


LINKS

Table of n, a(n) for n=3..25.
I. Barany and N. Tokushige, The minimum area of convex lattice ngons, Combinatorica, 24 (No. 2, 2004), 171185.
TianXin 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. 496518.
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 ngon, Geombinatorics, vol.II, 4(1993), p. 8588.
R. J. Simpson, Convex lattice polygons of minimum area, Bulletin of the Australian Math. Society, 42 (1990), p. 353367.


FORMULA

a(n)/2 = A063984(n) + n/2  1. [Simpson]
See Barany & Norihide for asymptotics.


CROSSREFS

See A089187 for the evenindexed 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)clubinternet.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



