

A089187


a(n) is the minimal area of a convex lattice polygon with 2n sides.


1



1, 3, 7, 14, 24, 40, 59, 87, 121, 164, 210, 274, 345, 430, 523, 632, 749, 890, 1039, 1222
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OFFSET

2,2


COMMENTS

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 ngon with one of its vertices so that different triangles get different labels (minimum taken over all triangulations). E.g. a(4)=7. Suppose a 4gon 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


REFERENCES

Stanley Rabinowitz, Convex Lattice Polygons, Ph.D. Dissertation (Polytechnic University, Brooklyn, New York, 1986).


LINKS

Table of n, a(n) for n=2..21.
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], 237240.
R. J. Simpson, Convex lattice polygons of minimum area, Bull. Austral. Math. Soc., 42[1990], 353367.


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 evenindexed subsequence of A070911. See also A063984.
Sequence in context: A173247 A123386 A060999 * A316319 A179178 A171973
Adjacent sequences: A089184 A089185 A089186 * A089188 A089189 A089190


KEYWORD

nonn,more


AUTHOR

Jamie Simpson (simpson(AT)maths.curtin.edu.au), Dec 07 2003


STATUS

approved



