# [seqfan] Re: Extension of A005646

Andrew Weimholt andrew.weimholt at gmail.com
Sat Dec 19 09:21:22 CET 2009

```On 12/18/09, Robert Munafo <mrob27 at gmail.com> wrote:

>  For the first 7 terms I am getting 1, 1, 1, 3, 6, 36, 112. So
>  obviously I have a ways to go (-:
>
>  Can you send me some kind of listing of the 26 unique taxonomies for N=6?
>
> [...]
>
>  If I can get this working I can probably confirm your N=8 number, as
>  my program currently takes about 8 minutes (and of course gets a
>

Hi Robert,

Thanks for looking at this.

The taxonomies for N=6 are shown below.
My program takes about 6 seconds to spit out a(7)=122,
and about 10 minutes to spit out a(8)=1015. If I let it run for several
hours (or days), it may be able to spit out a(9), but I'd like some
validation of my a(8) result before I tie up my CPU for that long :-)

(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2) | (0,1,3,4,5)
(3) | (0,1,2,4,5)
(4) | (0,1,2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2) | (0,1,3,4,5)
(3) | (0,1,2,4,5)
(0,4) | (1,2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2) | (0,1,3,4,5)
(3) | (0,1,2,4,5)
(0,1,4) | (2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2) | (0,1,3,4,5)
(0,3) | (1,2,4,5)
(1,4) | (0,2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2) | (0,1,3,4,5)
(0,3) | (1,2,4,5)
(1,2,4) | (0,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(0,2) | (1,3,4,5)
(1,3) | (0,2,4,5)
(0,2,4) | (1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2,3) | (0,1,4,5)
(2,4) | (0,1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(2,3) | (0,1,4,5)
(0,2,4) | (1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1) | (0,2,3,4,5)
(0,2,3) | (1,4,5)
(0,2,4) | (1,3,5)
-----------------
(0) | (1,2,3,4,5)
(0,1) | (2,3,4,5)
(2,3) | (0,1,4,5)
(2,4) | (0,1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1,2) | (0,3,4,5)
(1,3) | (0,2,4,5)
(1,4) | (0,2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1,2) | (0,3,4,5)
(1,3) | (0,2,4,5)
(0,1,4) | (2,3,5)
-----------------
(0) | (1,2,3,4,5)
(1,2) | (0,3,4,5)
(1,3) | (0,2,4,5)
(2,4) | (0,1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1,2) | (0,3,4,5)
(1,3) | (0,2,4,5)
(0,2,4) | (1,3,5)
-----------------
(0) | (1,2,3,4,5)
(1,2) | (0,3,4,5)
(0,1,3) | (2,4,5)
(1,2,4) | (0,3,5)
-----------------
(0) | (1,2,3,4,5)
(0,1,2) | (3,4,5)
(0,1,3) | (2,4,5)
(0,1,4) | (2,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(0,3) | (1,2,4,5)
(0,4) | (1,2,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(0,3) | (1,2,4,5)
(1,4) | (0,2,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(0,3) | (1,2,4,5)
(0,1,4) | (2,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(1,3) | (0,2,4,5)
(2,4) | (0,1,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(1,3) | (0,2,4,5)
(0,2,4) | (1,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(0,1,3) | (2,4,5)
(0,2,4) | (1,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2) | (1,3,4,5)
(0,1,2,3) | (4,5)
(0,1,2,4) | (3,5)
-----------------
(0,1) | (2,3,4,5)
(2,3) | (0,1,4,5)
(0,2,4) | (1,3,5)
-----------------
(0,1) | (2,3,4,5)
(0,2,3) | (1,4,5)
(0,2,4) | (1,3,5)
-----------------
(0,1,2) | (3,4,5)
(0,1,3) | (2,4,5)
(0,2,4) | (1,3,5)

Andrew

```