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

1,2

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.

Links

Table of n, a(n) for n=1..9.

Tim Cieplowski, Illustration of first few terms

Gordon Hamilton, $1,000,000 Unsolved Problem for Grade 8 (2011)

Example

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

Crossrefs

Cf. A226595.

Sequence in context: A310070 A036572 A139328 * A282731 A134919 A033437

Adjacent sequences: A253617 A253618 A253619 * A253621 A253622 A253623

Keyword

hard,more,nonn

Author

Tim Cieplowski, Jan 06 2015

Status

approved