Stroke sequence

[Max]

kohmoto wrote:

>     http://www.research.att.com/projects/OEIS?Anum=A089243
>     >  0,1,3,4,9,22,55
>     I want to know more terms of this sequence.

I don't understand definition of A089243.

First, "a star graph with n edges" sounds to me as undirected graph while the "stroke" is defined for directed graphs. And even if we assume that the edges of the star graph are somehow directed, in the example we see edges of both directions, e.g., 1->0 and 0->1 which is very confusing.

Second, the comment says "Two arrangements are considered the same if one is a rotation or reflection of the other". What "arrangements" it is talking about? In the example I see two partitions  {1->0, 2->0, 3->0} and {0->1, 0->2, 0->3} that looks like reflections of one another, aren't they?

>  
>     Once, I tried to calculate number of partitions into strokes of grid 
> graph n x n.

Please clarify what are strokes in your case and what partitions into strokes are considered the same.

Max

>  
>     1 x 1
>     .__.
>     |__| 
>  
>     Names of nodes
>     12
>     43
>  
>     Partitions into strokes : 12341, 1234+14, 123+143, 12+32+14+34, so 
> b(1)=4
>  
> 
>     2 x 2
>     .__.__.
>     |__|__| 
>     |__|__| 
>  
>     Names of nodes
>     123
>     456
>     789
>  
>     In this case, a partitions like 1236987458+14+25+5* exists. b(2)=?
>     If n=2 then it already becomes rather difficult.   
>  
>     I also want to know about b(n) sequence.
>     Does anyone have a good idea to search all the partitions into strokes?
>  
>     The idea "stroke" doesn't exist in graph theory, so I think it is 
> worth studying.
>  
>     Yasutoshi
>