[seqfan] Re: nice new board game puzzle A337663

[hv at crypt.org]

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

I don't see Arnauld's response there, do I need to do something special
to see it?

: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.)

This gets quite tricky: for n >= 5 we can have multiple independent starting
clusters, and it is not obvious to me how far away from each other those
can be.

Starting clusters can be independent only if they are the seed for the
placement of one of the numbers 2 to 8, so there can be no more than 7
of them. But that independence will make it a whole lot more difficult
to calculate for n >= 5.

My inclination is to keep them independent, and at each step consider
each possible way of placing two or more of them in relation to each
other (consistent with prior information) that might generate another
possible location for the next integer to be placed. (Taking care,
therefore, that no existing entry > 1 acquires a new neighbour. But
two 1s _can_ become neighbours.)

That sounds quite tough to code, and even tougher to make fast.

Hugo