[seqfan] Re: Alternating Vertical and Horizontal Moves In Grid

[Jonathan Post]

Pretty! These are so close to spacefilling (dragon curve like) that I
wonder what they look like in the limit, and how many squares in the
nxn are NOT included.

On Wed, Feb 25, 2009 at 11:33 AM, Giovanni Resta <g.resta at iit.cnr.it> wrote:
> Jaume Oliver i Lafont wrote:
>> The difference between these sequences starts 0,0,1,0,1,0,1,0...
>> so the second bisection of both sequences seems to be the same: 4,14,32,58,92...
>> This is not on the EIS, but one half of it appears only once, with a
>> simple closed form that makes sense to this problem.
>> http://www.research.att.com/~njas/sequences/?q=2,7,16,29,46
>>
>> Jaume
>>
> Well found, but, always under the condition that my program is correct,
> I found that for n=12, instead of 121 as in the sequence you linked, I
> got 134,
> for the start in the corner, with a nice spiral-like path. The
> computation for the
> "start anywhere" is slower, so I do yet not know where it goes, but it
> cannot be smaller
> than 134..
> I've updated the picture
> http://ilex.iit.cnr.it/resta/Leroy2.pdf
> to include the cases N=11 and N=12 (in the second page).
>
> giovanni
>
>
>
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