[seqfan] Re: Quick question about self-avoiding walks

Neil Sloane njasloane at gmail.com
Mon Mar 5 01:03:56 CET 2012

I just added this sequence: A209077. It could use some more terms!

On Sat, Dec 10, 2011 at 9:30 AM, Jon Wild <wild at music.mcgill.ca> wrote:

> On Sat, 10 Dec 2011, Alonso Del Arte wrote:
>  Does the OEIS have the sequence of the number of distinct self-avoiding
>> walks possible on an n^2 lattice where every vertex is visited? Here is an
>> example of what I'm talking about:
>> http://oeis.org/wiki/File:**Walks_on_8_by_8_SqLattice.png<http://oeis.org/wiki/File:Walks_on_8_by_8_SqLattice.png>I would look it up
>> myself but I don't know the proper word for it nor have I thought about
>> how
>> to calculate terms.
> Look for Hamiltonian cycles on a square grid. They're only possible for
> squares of even side. Sequence A003763 is the main version and it
> references A120443, A140519 and A140521.
> I looked for these once before and found the OEIS didn't have the version
> of the sequence reduced for symmetry i.e. where rotations and reflections
> are not counted as distinct. I have the first few terms if anyone wants to
> submit the sequence:
> 2x2: 1 rook's tour
> 4x4: 2 rook's tours
> 6x6: 149 rooks tours
> 8x8: 580717 rook's tours
> --Jon
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Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

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