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

2,1

Comments

Worthy of consideration to introduce slopes in the math classroom.

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

Links

Table of n, a(n) for n=2..6.

Hiroaki Yamanouchi, Examples

Giovanni Resta, Illustration of a(7)>=23 and a(8)>=29

Example

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 . .

Crossrefs

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

Sequence in context: A094913 A265060 A320849 * A020678 A310034 A014811

Adjacent sequences: A255978 A255979 A255980 * A255982 A255983 A255984

Keyword

nonn,more

Author

Gordon Hamilton, Mar 13 2015

Extensions

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

Status

approved