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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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