A345648 - OEIS

%I #8 Jun 22 2021 12:26:10

%S 0,0,24,228,904,2788,5880,13008,22120,37976,58584,95472,125016,195816,

%T 255064,337916,444760,611760,719800,978388,1127088,1411756,1736776,

%U 2174584,2389552,2995336,3504768

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

%C 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.

%C See A345459 for images of the polygons.

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

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

%K nonn,more

%O 0,3

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jun 21 2021