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A089187 a(n) is the minimal area of a convex lattice polygon with 2n sides. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
For polygons with an odd number of sides see A070911.
LINKS
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).
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
KEYWORD
nonn
AUTHOR
Jamie Simpson, Dec 07 2003
EXTENSIONS
a(22) onwards from Günter Rote, Sep 17 2023
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)