A345648 Number of polygons formed outside an n X n square when connecting all 4n points on the perimeter of the square by infinite lines.

0, 0, 24, 228, 904, 2788, 5880, 13008, 22120, 37976, 58584, 95472, 125016, 195816, 255064, 337916, 444760, 611760, 719800, 978388, 1127088, 1411756, 1736776, 2174584, 2389552, 2995336, 3504768

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Jun 21 2021

Keywords

• nonn
• more

Comments

For n = 0 to n = 11 the number of polygons formed outside the n x n square is less than the number formed inside the square. This changes for n >= 12 when the number formed outside becomes greater. The ratio of the number of polygons outside to the number inside for n = 26 is about 1.07 . If this ratio is unbounded or approaches some finite value as n -> infinity is not known.

See A345459 for images of the polygons.

Crossrefs

Cf. A345459 (number inside and outside with square), A255011 (number inside the square), A344993, A344857, A092098, A007678.

Formula

a(n) = A345459(n) - A255011(n).