[seqfan] Re: Kaku-Stroke-Bus route

[Giovanni Resta]

On 06/14/2016 05:20 AM, zbi74583.boat at orange.zero.jp wrote:
>      Hi,Seqfans
>
>      "Bus route" is the same thing as "Stroke" on non directed graph.
>      See the definition on A131709
>
>      To compute number of partition of graph into "Bus route" is rather difficult
> even if graph is easy as follows.
>
>      nxn grid  See A135442
>      K_n       See A135444
>      Could anyone confirm them and compute more term?

I think I have some difficulties understanding the
definition and/or reconcile A131709 and A135442.

A131709  is Number of partitions into "bus routes" of an n X 1 grid.
while
A135442 Number of partitions into "bus routes" of n X n grid.

but why A131709(1) = 14   and A135442(1) = 4   ?

They should be equal unless the two sequences uses a different
definition of "partitions into bus routes".

I have also some difficulties understanding the nature
of bus routes.  It seems they are directed paths.

However, in A135444 (Number of partitions into "bus routes" of K_n.)
we have a(2)=1.
If the routes are directed, I would have expected a(2)=2, because there
are two routes:  1 => 2 and 2 => 1.

Probably there is something that I do not grasp. Is it possible to have 
a list of the 14 (or 4 ??) partitions of the grid 1 X 1 and/or the 3 
partitions of K_3, to better understand ?

Giovanni