[seqfan] Re: Toothpick sequences (again) (from Richard Mathar by way of admin)

[Benoît Jubin]

Apparently you're right: this gives the right terms for A160160 (and
A160161), and if I didn't make a mistake, the next two terms are 151,
215 (respectively 64, 64).

It might be worth looking at other dimensions:
-2D: (A139250,A139251)
-3D: (A160160,A160161)
I think the 1D equivalent is (A006046,B), where B(n)=2^A000120(n).
I also think that the d-dimensional equivalent for the
first-difference sequence begins with
1,2,4...2^d (no-obstruction phase), then 2^d d more times, and then
consists only of multiples of 2^d.

Benoit



On Wed, Jun 3, 2009 at 10:49 PM,  <franktaw at netscape.net> wrote:
> I haven't checked in detail, but I suspect what is happening is a
> rotation of axes.  The first toothpick is oriented with the x axis.
> Then ones are placed on its ends, aligned with the y axis.  The third
> generation is aligned with the z axis, and then it loops back to the x
> axis.  As before, a toothpick is only placed when there is a single end
> at a point, not when there are two meeting there (more than two is
> impossible).
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Benoît Jubin <benoit.jubin at gmail.com>
>
> 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> Benoît 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>
>> 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> ...
>> ...
> ...
>> Basically A160160, A160170, A160408 remain completely obscure also to
> me.
>
> For me too, as well as A160120.  Anyone?
>
>
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