[seqfan] Extension of A005646

[Robert Munafo]

Andrew,

I've written a program, but haven't quite gotten the algorithm worked
out (since I don't have access to the cited articles, all I have to go
on is "A 'classification' is a set of n type-specimens each one of
which is corralled on its own by the union of a set of binary
partitions, none of which could be omitted without leaving 2 types
unseparated")

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?

I suspect that I am treating two classifications as distinct when
complementing one of more of their constituent binary partitions would
make them equivalent, but not clear on how to detect or avoid. No idea
yet why N=7 might be wrong but I should correct N=6 first.

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
totally incorrect answer)

Andrew Weimholt wrote:
> I get A005646(8) = 1015
>
> Anyone want to confirm?
>
> Andrew

-- 
  Robert Munafo  --  mrob.com