Stroke sequence

[kohmoto]

    Hello Seqfans.


    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.



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

    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
 
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