A253620 Maximum number of segments in nonintersecting increasing path on n X n hexagonal (isogonal) grid.

0, 3, 6, 10, 14, 19, 25, 30, 36

Offset: 1

Author

Tim Cieplowski, Jan 06 2015

Keywords

• hard
• more
• nonn

Comments

The path cannot intersect itself, not even on single points. "Increasing" means that the (Euclidean) length of each segment must be strictly greater than that of the previous one.

The analogous sequence for a triangular (isogonal) grid seems to satisfy a(n) = 2n+1, with 2^(n-2) such paths up to isomorphism.

Examples

			An example for a(4) = 10
       .   .   .   .
    09   .   .   .   .
  01   .   .   .   .   .
00  07   .   .   .   .  10
  02  05   .   .   .  08
     .   .   .   .  06
      03   .   .  04
		

Links

• Tim Cieplowski, Illustration of first few terms
• Gordon Hamilton, $1,000,000 Unsolved Problem for Grade 8 (2011)

Crossrefs

Cf. A226595.