A255981 a(n) = greatest number of edges in a simple polygon on an n X n grid with no two edges parallel.

3, 5, 8, 12, 17

Offset: 2

Author

Gordon Hamilton, Mar 13 2015

Keywords

• nonn
• more

Comments

Worthy of consideration to introduce slopes in the math classroom.

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

Examples

			a(3) = 5 because of this quadrilateral in a 3 x 3 square:
                    1 2 .
                    . 4 .
                    5 . 3
a(4) = 8 because of this polygon:
                   1 3 . 4
                   . . 2 6
                   . . 5 7
                   . 8 . .
		

Links

• Hiroaki Yamanouchi, Examples
• Giovanni Resta, Illustration of a(7)>=23 and a(8)>=29

Crossrefs

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

Extensions

a(5)-a(6) corrected by Hiroaki Yamanouchi, Mar 14 2015