[seqfan] Re: Knights-move Ulam-Warburton - nice problem

[David Seal]

A small point I'm wondering about for A319018: why does it have offset 0 and start with 0? Surely if one starts with a grid having no ON cells, *every* subsequent generation also has no ON cells, and so the sequence is just A000004?

Best regards,

David Seal


> On 16 December 2018 at 17:08 Neil Sloane <njasloane at gmail.com> wrote:
> 
> 
> Dear Seq Fans, Someone who watched the Terrific Toothpicks Numberphile
> video on Youtube suggested a knights-move version.  I looked this up in the
> OEIS of course and found that Remy Sigrist had already studied it. The
> illustrations (excluding mine) are lovely, and so is the problem.
> The original sequences are A319018, A319019; while trying to analyze it I
> added three more last night, A322048, -049, -050.
> 
> The main problem to crack is what is A322049.(which gives the growth from
> the corners of the octagon after a power of 2 generations)?
> 
> It would be nice to have a really big b-file (or a-file or both) for
> A322050.
> 
> Another question: look at the rows of the triangle in A322050. They are
> converging to the sequence A322049. The number of terms in rows 1,2,3,4,...
> that agree with the limit are 1,1,2,4,7,11,22 (I think). How does this
> continue? This is not yet in the OEIS.
> 
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