[seqfan] Re: "OEIS Sampler" handouts for San Diego Meeting

Kevin Ryde user42 at zip.com.au
Sat Dec 22 00:40:31 CET 2012


njasloane at gmail.com (Neil Sloane) writes:
>
> http://www.polprimos.com/imagenespub/poltp4d4.jpg
>
> What would your corresponding figures look like?

Ascii art below :).

Plot a toothpick only as a point at its middle, then draw lines from
that point to its children in the next growth level.

Or equivalently draw a half of a toothpick only if it gets a new
toothpick added at that end in the next growth level.

I arrived at this contemplating how toothpicks are successively added.
Drawing just points helped me see the structure.  Toothpick ends can
touch existing toothpicks and when that happens you have to look
carefully to see what grew from where.

I suppose the net effect is to chop off terminating ends.  If ends are
thought of as part of the tree then it'd be a chopping-off one level of
leaf nodes.  Perhaps there's a graph theory name for such a chop.



                             *     *     *--*     *--*
                             |     |        |     |
         *      *--*--*      *--*--*        *--*--*
         |         |            |              |
   *     *         *            *              *
         |         |            |              |
         *      *--*--*      *--*--*        *--*--*
                             |     |        |     |
                             *     *     *--*     *--*
   1     3         7            11             15



   *           *       *--*--*     *--*--*
   |           |          |           |
   *--*     *--*          *--*     *--*
   |  |     |  |          |  |     |  |
   *  *--*--*  *       *--*  *--*--*  *--*
         |                      |
         *                      *
         |                      |
   *  *--*--*  *       *--*  *--*--*  *--*
   |  |     |  |          |  |     |  |
   *--*     *--*          *--*     *--*
   |           |          |           |
   *           *       *--*--*     *--*--*
         23                     35



  *     *     *     *
  |     |     |     |
  *--*--*     *--*--*
     |           |
     *--*     *--*
     |  |     |  |
  *--*  *--*--*  *--*
           |
           *
           |
  *--*  *--*--*  *--*
     |  |     |  |
     *--*     *--*
     |           |
  *--*--*     *--*--*
  |     |     |     |
  *     *     *     *
           43



The quadrants at the 43 stage start to show the replication.  Eg the
first quadrant

    4     3
    |     |     middle toothpicks A,B
    4--B--3     replicated parts 1,2,3,4
       |
    1--A
    |  |
    1  2--2


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