[seqfan] Re: Hamiltonian cycles on n X m square grid of points.

[Neil Sloane]

Certainly  subit the general result - it is a symmetric array, so you could
do it as an infinite
table read by antidiagonals (that's probably the best),
or, throw away the redundant half and make it into a triangle read by rows.

By the way, are you sure that neither of these is presently in the OEIS?
(I thought we have one of them, but I could be wrong)

Best regards
Neil

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



On Mon, Jan 7, 2019 at 11:17 PM Robert FERREOL <robert.ferreol at gmail.com>
wrote:

> Hello,
>
> On https://oeis.org/A003763  are counted the Hamiltonian cycles on 2n X
> 2n  square grid of points
>
> and on https://oeis.org/A222200  the case n+1 X n
>
> It's missing the general case n X m ..
>
> I did this research , but UP TO SYMMETRIES :
>
> Case 2 X 2 : 1
>
> Case 3 X 2 : 1
>
> Case 3 X 3 : 0
>
> Case 4 X 3 : 1 :
>
> Case 4 X 4 : 2 : and
>
> Case 5 X 2 :
>
>
> Case 5 X 3 :  0
>
>
> Case 5 X 4 :   5
>
> Case 5 X 5 : 0
>
> Case 6 X 2 : 1 (obvious)
>
> Case 6 X 3 :   2
>
>
> Case : 6 X 4 :  15 :
>
> ase : 6 X 5 : 44 :
>
> Case : 6 X 6 :  ????   > A003763(3)/8=134 ....
>
>
> Could I begin a new sequence ???
>
>
>
> --
>
> ROBERT FERRÉOL
> 6, Rue des Annelets 75019 PARIS
> 01 42 41 91 98
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>
>
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