# [seqfan] Re: A139250 Question

P. Michael Hutchins pmh232 at gmail.com
Thu Mar 15 15:07:35 CET 2018

```First, I apologize for sounding like I doubted that the pattern of the
toothpick sequence had been found.  I read the Boise Math Circles statement
as saying that the students found the pattern, and I did doubt that.  But
even given that apparent misreading, I should have researched further

I have no business doubting an assertion by a member or associate of OEIS,
unless I can give sufficient reason.

My context was that I had been looking for such a result, and hadn't been
able to find one.  I thought that if there was one, it would be mentioned
on the A139250 page, if not the Boise Math Circles page - but I hadn't
found it there.  And I hadn't found the paper in which the solution appears.

A more thoughtful and considerate way of putting it is just to ask for a
pointer to the solution.

(I was excited to find the solution, since I had worked on it quite a bit,
and come up empty - although I thought I saw some regularity at the scale
of the 2^n-length subsequences.)

On Thu, Mar 15, 2018 at 4:39 AM, Neil Sloane <njasloane at gmail.com> wrote:

> M Hutchins said
>
> "
> There it says "By carefully keeping track of the toothpicks at each stage,
> we figured out a way to generate all the numbers in the ‘toothpick
> sequence’ using previously calculated numbers. This means, we found a
> recursive pattern in the sequence of numbers."."
>
> Me:  yes, that is correct, why do you doubt it?  The article you should
>
> David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence
> and Other Sequences from Cellular Automata
> <http://neilsloane.com/doc/tooth.pdf>, which is also available at
> arXiv:1004.3036v2 <http://arxiv.org/abs/1004.3036>
>
> (There are two links to different copies of the same article)
>
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Email: njasloane at gmail.com
>
>
> On Wed, Mar 14, 2018 at 6:16 PM, P. Michael Hutchins <pmh232 at gmail.com>
> wrote:
>
> > A139250 has a link, http://boisemathcircles.org/bmc-sessions/toothpicks.
> >
> > There it says "By carefully keeping track of the toothpicks at each
> stage,
> > we figured out a way to generate all the numbers in the ‘toothpick
> > sequence’ using previously calculated numbers. This means, we found a
> > recursive pattern in the sequence of numbers.".
> >
> > Is that in fact the case?
> >
> > --
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> >
>
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>
```