login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226596 Lengths of maximal non-crossing and non-overlapping increasing paths in n X n grids. 2
0, 2, 4, 7, 10, 13, 16, 20, 22 (list; graph; refs; listen; history; text; internal format)
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(n-1).

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 07:18 EST 2019. Contains 329914 sequences. (Running on oeis4.)