# [seqfan] Re: confused about toothpick sequence A139250!

Benoît Jubin benoit.jubin at gmail.com
Wed Apr 15 22:52:44 CEST 2009

> My conjectured definition gives a(4) = 11, not 13.

My definition also gives a(4)=11 and the same terms, at least up to
n=8.  Sorry, our emails crossed.

>
> - Each new toothpick must lie in the X direction or the Y direction
> - Two toothpicks may never cross
> - Each new toothpick must have its MIDPOINT
>    touching the ENDPOINT of EXACTLY ONE existing toothpick
>
>
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of N. J. A. Sloane
> Sent: Wednesday, April 15, 2009 4:06 PM
> To: seqfan at list.seqfan.eu; seqfan at seqfan.eu
> Cc: njas at research.att.com
> Subject: [seqfan] Re: confused about toothpick sequence A139250!
>
> There were several responses to my request for a precise definition
> of A139520, but none of them really satisfied me.
>
> I still do not understand the definition.
>
> A toothpick is a copy of the closed interval [0,1].
>
> Given a configuration of toothpicks in the plane.
>
> At the next step we add as many toothpicks as possible,
> subject to certain conditions.
>
> - Each new toothpick must lie in the X direction or the Y direction
> - Two toothpicks may never cross
> - Each new toothpick must have at least one of its endpoints
>    touching the midpoint of an existing toothpick
>
> That is not enough (it gives 1,3,7,13,21,...), so there
> must be an additional rule.  I can think of several versions,
> which is why I asked the question in the first place.
> I repeat, what is the precise definition of A139250?
>
> Neil
>
>
>
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