Discrete Mathematics Level pending

Let $$G$$ be a rectangular grid of unit squares with 3 rows and 8 columns. How many self-avoiding walks are there from the bottom left square of $$G$$ to the top left square of $$G$$?

Details and assumptions

A self-avoiding walk on a rectangular grid of unit squares is a sequence of moves between horizontally or vertically adjacent squares that does not visit the same square more than once.

The walk does not need to touch all the squares of $$G$$.

Since the grid has 3 rows, the top left and bottom left squares have exactly one square between them.

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