[seqfan] Re: Simple sequence not in the OEIS?

[Neil Sloane]

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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