There is a $3 \times 3$ tile such that the colors of the 9 unit cells are distinct. How many different ways are there to divide this tile into one or more pieces? ( We can only divide along the common edges of the unit cells.)
The official answer is $1434$. I have tried the recursive method but it seems not working for me and from $2\times2$ to $2\times3$ I encountered some problems.
I found a related discussion here: In how many different ways can a 9-panel comic grid be used? . However, the ways did not include the "L" shape (of course, it is used in comics...). Is there an effective way to calculate the possible ways in this question? Thank you very much.
