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

[Jon Wild]

On Sun, 11 Dec 2011, Benoît Jubin wrote:

> On Sat, Dec 10, 2011 at 6:30 AM, Jon Wild <wild at music.mcgill.ca> wrote:
>> 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.
>
> Jon, are these the same as meanders where you forbid the two types of
> tiles made of two quarter-circles?  If yes, this would be worth
> mentioning, and maybe using a (probably easy) modification of your
> program to illustrate them.

Yes, exactly - I did this already, thinking of these restricted meanders 
as "rook's tours", and when I looked the sequence up I found they appeared 
already in the oeis as these Hamiltonian circuits. I didn't know whether 
it was worth submitting the symmetry-reduced version of the sequence. But 
sure, I'll upload some pictures to illustrate A003763, and a link between 
this and A200000.

If I add tiles with a dead end, I can probably get the self-avoiding walks 
fairly easily, too--though I see Chris Gribble already has a program for 
this.

Jon