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Search: id:A089187
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| A089187 |
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a(n) = minimal area of a convex lattice polygon with 2n sides. |
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+0
2
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| 1, 3, 7, 14, 24, 40, 59, 87, 121, 164, 210, 274, 345, 430, 523, 632, 749, 890, 1039, 1222
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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For polygons with an odd number of sides see A070911.
This is also equal to the minimum number of ways to label each triangle of a triangulation of an n-gon with one of its vertices so that different triangles get different labels (minimum taken over all triangulations). E.g. a(4)=7. Suppose a 4-gon ABCD is triangulated with triangles ABC and ACD. If ABC is labeled B, then ACD can be given 3 possible labels, while if ABC is labeled A or C, only 2 labels are available for ACD and 3+2+2=7. - Johan Wastlund (jowas(AT)mai.liu.se), Aug 28 2007
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REFERENCES
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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.
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EXAMPLE
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The first entry is 1 because the convex lattice quadrilateral of minimal area is a unit square. The minimal area hexagon has area 3.
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CROSSREFS
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The even-indexed subsequence of A070911. See also A063984.
Sequence in context: A093523 A123386 A060999 this_sequence A004006 A089240 A057524
Adjacent sequences: A089184 A089185 A089186 this_sequence A089188 A089189 A089190
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KEYWORD
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more,nonn
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AUTHOR
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Jamie Simpson (simpson(AT)maths.curtin.edu.au), Dec 07 2003
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