[seqfan] Re: Toothpick sequences (again) (from Richard Mathar by way of admin)
benoit.jubin at gmail.com
Thu Jun 4 06:03:44 CEST 2009
On Tue, Jun 2, 2009 at 8:03 AM, Olivier Gerard <olivier.gerard at gmail.com> wrote:
> From Richard Mathar:
> Benoit wrote in http://list.seqfan.eu/pipermail/seqfan/2009-May/001532.html
> bj> BenoÃ®t Jubin benoit.jubin at gmail.com
> bj> Thu May 28 02:34:32 CEST 2009
> bj> ...
> bj> Does anyone know the definitions used for the "3d toothpick sequences"
> bj> A160160, A160161, A160120, A160121, A160170, A160171?
> bj> The author is in copy to this email, and I'd like to politely remind
> bj> him that submissions are not "guess-my-sequence" puzzles.
> bj> ..
> One might define a 3D version of the toothpick sequence by
> (i) place the first toothpick aligned with any of the Cartesian axes of the
> cubic grid.
> (ii) For the step from generation n to n+1 define the exposed
> toothpick ends as those 3D points which are one of the two end points
> defined by one (and only one, not shared by another) of the toothpicks in
> generation n and which are not a midpoint of any toothpick of generation n.
> (iii) Add in generation n+1 at each of the exposed points marked
> in step (ii) a cross (=of two toothpicks) in the plane perpendicular to the
> toothpick that defined the exposed point.
> This should (I guess, should be checked !) start the count of
> toothpicks (crosses
> contain 2 of them, counted individually) as
I didn't check the sequence, but for n>1, this is 16*(n-2)+5, which
would be a less interesting behaviour than in 2D. What about higher
> Basically A160160, A160170, A160408 remain completely obscure also to me.
For me too, as well as A160120. Anyone?
More information about the SeqFan