counting strokes

[y.kohmoto]

    to Edwin :
    Thank you for a polite message.
    Don't mind that your response will be later.

    I feel that I should enumerate numbers of partitions into strokes on
perfect graph, n*n grid graph, triangle grid graph etc, but those problem
are complicated.

    For example, n*n grid :
    n=1 , number of partitions into strokes = 9
    n=2, I tried to calculate it,  but I haven't got the number, maybe
several  hundred?

    Yasutoshi