[seqfan] Re: nice new board game puzzle A337663

Peter Kagey peterkagey at gmail.com
Thu Oct 8 08:11:20 CEST 2020


I posted this question to Code Golf Stack Exchange, and Arnauld Chevallier confirmed the given terms: https://codegolf.stackexchange.com/a/212164/53884 <https://codegolf.stackexchange.com/a/212164/53884>

Arnauld gives this illustration for a(4):
 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 . 35 18 36  . 23  . 21  . 32  .  .  .  .  .
 .  . 17  1  . 14  9  . 12 20  .  .  .  .  .
 .  . 34 16 15  .  5  4  8  .  . 26 27  .  .
 .  .  .  . 31  . 10  1  3 19 25  .  1 28  .
 .  .  .  .  .  . 11  .  2  6  . 33  . 29  .
 .  .  .  .  .  . 24 13 22  1  7  .  .  .  .
 .  .  .  .  .  . 37  .  . 30 38  .  .  .  .
 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
My suspicion is that it will be hard to get more many terms because of how quickly the search space grows.

This is a really lovely sequence. I’d be interested to know more about this, such as:
What is the “widest” such a game can get? (The above example uses 13 columns.)
How many maximal games?
What are analogs of this on a hexagonal tiling, triangular tiling, or in higher dimensions?
Is this interesting to investigate on graphs other than grids?

pk

> On Oct 7, 2020, at 10:18 AM, Neil Sloane <njasloane at gmail.com> wrote:
> 
> needs more terms
> 
> and actually the given terms need checking
> 
> --
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