Number of ways of tiling a 3*N board with 2*1 dominoes problem
These two cases are already counted in the recursive calls g(n-1).

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A****
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g(n-1)


g(n-1) counts all possibilities to fill the empty space in this ^ form. One way would be to fill it out like the following image, so this case already gets counted and you don't need to add another recursive call.

AC***
AC***
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