

A288247


2 * smallest possible area of a simple nsided lattice polygon whose vertex coordinates x and y are both independent permutations of the integers 1 ... n, subject to the condition that none of its edges are mutually parallel.


4



3, 2, 3, 8, 9, 7, 9, 8, 11, 12, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21
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OFFSET

3,1


COMMENTS

It is conjectured that a(n) = n2 for all n > 15, i.e. the bound of Pick's theorem is achievable for all larger n.
Results are partially based on the discussion in the newsgroup dxdy.ru, see link.


LINKS

Table of n, a(n) for n=3..23.
Michael Collier, Dmitry Kamenetsky, Herbert Kociemba, Tom Sirgedas, Al Zimmermann  Polygonal Areas. Discussion in newsgroup dxdy.ru.
Hugo Pfoertner, Minimum Area Lattice Polygons, Illustrations for n = 3 ... 11.
Markus Sigg, Javascript visualization of lattice polygons. Example showing the minimal 9sided polygon.
Wikipedia, Pick's theorem.
Al Zimmermann's Programming Contests, Polygonal Areas.


CROSSREFS

Cf. A288248, A288249.
Sequence in context: A131134 A151690 A346472 * A143744 A095243 A049921
Adjacent sequences: A288244 A288245 A288246 * A288248 A288249 A288250


KEYWORD

nonn,more


AUTHOR

Hugo Pfoertner, Jun 07 2017


STATUS

approved



