A255981 - OEIS

%I #16 May 05 2016 10:54:42

%S 3,5,8,12,17

%N a(n) = greatest number of edges in a simple polygon on an n X n grid with no two edges parallel.

%C Worthy of consideration to introduce slopes in the math classroom.

%C a(7) >= 23 and a(8) >= 29, see illustration in Links.

%H Hiroaki Yamanouchi, <a href="/A255981/a255981.pdf">Examples</a>

%H Giovanni Resta, <a href="/A255981/a255981.png">Illustration of a(7)>=23 and a(8)>=29</a>

%e a(3) = 5 because of this quadrilateral in a 3 x 3 square:

%e                     1 2 .

%e                     . 4 .

%e                     5 . 3

%e a(4) = 8 because of this polygon:

%e                    1 3 . 4

%e                    . . 2 6

%e                    . . 5 7

%e                    . 8 . .

%Y Cf. A271449. Construction perhaps related to construction of Costas arrays: A008404.

%K nonn,more

%O 2,1

%A _Gordon Hamilton_, Mar 13 2015

%E a(5)-a(6) corrected by _Hiroaki Yamanouchi_, Mar 14 2015