[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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