

A070911


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


2




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..10.
Barany & Norihide, The minimum area of convex lattice ngons
Cai, On the minimum area of convex lattice polygons
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.
Sequence in context: A232603 A069480 A100613 * A113240 A098376 A028259
Adjacent sequences: A070908 A070909 A070910 * A070912 A070913 A070914


KEYWORD

easy,nice,more,nonn,changed


AUTHOR

Pierre Bornsztein (pbornszt(AT)clubinternet.fr), May 20 2002


EXTENSIONS

Additional comments from Steven Finch, Dec 06 2003


STATUS

approved



