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

Rob Pratt Rob.Pratt at sas.com
Wed Apr 15 22:19:29 CEST 2009

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

- 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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```