

A226596


Lengths of maximal noncrossing and nonoverlapping increasing paths in n X n grids.


2




OFFSET

1,2


COMMENTS

The path is allowed to touch but not cross itself on single points, but not on segments of any length. "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..9.
Giovanni Resta, Illustration of a(2)a(9)
Gordon Hamilton, $1,000,000 Unsolved Problem for Grade 8 (2011)


FORMULA

a(n) <= A160663(n1).


EXAMPLE

A solution for the case a(8)=20 is

01 02 . . . . . 16
.. . 03 . . . . 14
09 . 15 . 05 . . 12
.. . 04 . . . . .
.. . 06 13 . 07 . 21
.. . 08 . 11 . . 19
10 . . . . . . 17
20 18 . . . . . .



CROSSREFS

Cf. A226595.
Sequence in context: A033627 A066512 A304116 * A135678 A001195 A295513
Adjacent sequences: A226593 A226594 A226595 * A226597 A226598 A226599


KEYWORD

nonn,hard,more


AUTHOR

Charles R Greathouse IV and Giovanni Resta, Jun 13 2013


STATUS

approved



