A226595 Lengths of maximal nontouching increasing paths in n X n grids.

0, 2, 4, 7, 9, 12, 15, 17, 20, 24, 27, 29, 33, 36, 39

Offset

1,2

Comments

The path is not allowed to touch itself, not even on single points. "Increasing" means that the (Euclidean) length of each line segment must be strictly longer than the last.

Links

Table of n, a(n) for n=1..15.

Giovanni Resta, Illustration of a(2)-a(9)

Bert Dobbelaere, C++ program

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

Stan Wagon, Illustration for a(2)-a(12)

Formula

a(n) <= A226596(n) <= A160663(n-1).

Example

An example for a(8)=17
-------------------------
01 02  .  .  .  . 05  .
..  . 03  . 04  .  . 18
09 07  .  . 06  .  . 16
..  .  .  .  .  .  . 14
..  .  .  .  .  .  . 12
..  . 08  .  .  .  .  .
10 17 15 13  .  .  .  .
..  .  .  . 11  .  .  .
-------------------------

Crossrefs

Cf. A226596.

Sequence in context: A184735 A184583 A189379 * A031435 A065560 A134886

Adjacent sequences: A226592 A226593 A226594 * A226596 A226597 A226598

Keyword

nonn,hard,nice,more

Author

Charles R Greathouse IV and Giovanni Resta, Jun 13 2013

Extensions

a(10)-a(12) from Joseph DeVincentis via Charles R Greathouse IV, Oct 08 2015

a(13) from Charles R Greathouse IV, Oct 25 2015 using code from Joseph DeVincentis

a(14)-a(15) from Bert Dobbelaere, Oct 05 2018

Status

approved