[seqfan] Re: Simple sequence not in the OEIS?
Neil Sloane
njasloane at gmail.com
Wed Jun 7 17:46:49 CEST 2023
Hi Lars! If you consider closed paths (as opposed to open paths) then n
must be even, and there is A209077. These would be called Hamiltonian
cycles (or paths).
On Wed, Jun 7, 2023 at 10:25 AM Lars Blomberg <lars.blomberg2 at hotmail.com>
wrote:
> Hello Seqfans,
>
> I have been looking at how many different space filling paths there are in
> a n x n lattice, starting from the SW corner in the N direction, and
> stepping in N,S,E,W directions only, counted up to rotations and
> reflections.
>
> There are 3 solutions for n=3:
> +--+--+ +--+--+ +--+ +
> | | | | | | |
> + + + + +--+ + + +
> | | | | | | | |
> + +--+ + +--+ + +--+
>
> The sequence starts with n=2: 1, 3, 23, 347, 10199, 683227, ...
>
> What puzzles me is that such a relatively simple sequence is not present
> in OEIS even though there are a great many sequences concerning paths on
> square lattices.
>
> Maybe I have made some stupid mistake.
> Any clarifying information will be appreciated.
>
> /Lars B
>
>
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>
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