login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288247 2 * smallest possible area of a simple n-sided 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

It is conjectured that a(n) = n-2 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 9-sided 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 26 05:58 EDT 2021. Contains 348257 sequences. (Running on oeis4.)