games born on day n

[Richard Guy]

Dean is quite right, and there should be two sequences.

All games are `born again' each day after their birthday.

David Wolfe, Dan Calistrate & Marc Paulhus have
shown that (all) the games born on day  n  form a
distributive lattice.  A paper will appear in
More Games of No Chance, the proceedings of the
2000 Workshop at eMiSaRI.

Newborn games:  1  3  18  1452  ...

Games:          1  4  22  1474  ...

The number of levels in the lattice (another
recordable sequence?)

                1  3   9    45   2949   ...

is one more than twice the (total) number
of games born on the previous day.

Best,   R.

On Wed, 21 Nov 2001, Dean Hickerson wrote:

> > Will some fanster put this into the approved
> > shape for Neil ?  Thanks!
> 
> I'll do it in a few days if noone does it first.  (I don't have my
> references handy at the moment.)
> 
> > The following is the sequence of numbers of games
> > born on days 0, 1, 2, 3.
> 
> That should probably be "on or before".  E.g. the 4 games on day 1 include
> the one from day 0 and 3 new ones.  Perhaps the sequence (1 3 18 1452) that
> counts the new ones on day n should also be included.
> 
> > 1 4 22 1474
> 
> For what it's worth, Robert Li and I also counted 1474 games on day 3 when
> we were grad students at Berkeley in 1974.  We were working without a
> computer, and made no attempt to count the day 4 games.
> 
> Dean Hickerson
> dean at math.ucdavis.edu