[seqfan] Integers tiling the plane

[Eric Angelini]

Hello SeqFans,
This link is for people reading French, sorry.
It deals with the following  idea.
Take an infinite plane tiled by initially
empty squares of size 1 x 1;
Law1: such a square can only be filled
by a one-digit integer d;
Law2: we call "neighborhood" of d the
3 x 3 square centered on d;
Law3: if d occupies a square, there
must be in the neighborhood of d
exactly d copies of d.
(...)
Two hard questions:
1) how does the sequence of integers
tiling the plane start? I think it starts
with 9, 99, 366, 636, 663, 999, 1888,...
2) how many different boxes of size
n x n x n can be filled if the neighborhood
is now defined by the 3 x 3 x 3 cube
centered on d? (I cannot even count
the ways a 2 x 2 x 2 box can be
filled...)
Best,
E.
<http://www.cetteadressecomportecinquantesignes.com/Paveur.htm>http://www.cetteadressecomportecinquantesignes.com/Paveur.htm