[seqfan] Re: confused about toothpick sequence A139250!

[franktaw at netscape.net]

Actually, the configurations aren't all that different.  Start with 
one, rotate each toothpick a quarter-turn, and then rotate the whole 
configuration a quarter turn, and you get the other one.

Franklin T. Adams-Watters


-----Original Message-----
From: Benoît Jubin <benoit.jubin at gmail.com>

Actually, two "dual" definitions give this sequence: the one I gave
below (which is essentially the same as Rob Pratt's), and Neil's, when
you add toothpicks such that exactly (and not "at least") one of their
endpoints is the middle of an existing toothpick.  The two sequences
of configurations obtained are different, but the numbers of
toothpicks are the same (at least up to a(8)=43).  This is a
noteworthy fact, and I don't see an immediate argument to prove it.

The sequence corresponding to Neil's original definition (with "at
least") is n^2-n+1, because there will be no hole left in the grid.

Benoit