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Search: id:A070911
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| A070911 |
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a(n) is twice the least possible area enclosed by a convex lattice n-gon. |
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+0
3
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OFFSET
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3,2
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COMMENT
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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
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REFERENCES
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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.
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LINKS
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Barany & Norihide, The minimum area of convex lattice n-gons
Cai, On the minimum area of convex lattice polygons
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FORMULA
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a(n)/2 = A063984(n) + n/2 - 1 [Simpson]
See Barany & Norihide for asymptotics.
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CROSSREFS
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See A089187 for the even-indexed subsequence. See A063984 for further information.
Sequence in context: A057683 A069480 A100613 this_sequence A113240 A098376 A028259
Adjacent sequences: A070908 A070909 A070910 this_sequence A070912 A070913 A070914
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Pierre Bornsztein (pbornszt(AT)club-internet.fr), May 20 2002
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EXTENSIONS
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Additional comments from S. R. Finch, Dec 06 2003
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