On an infinitely large chessboard, in how many paths of length $10$ can a knight take and end up in its original position? https://ift.tt/eA8V8J

The knight is moved exactly $10$ times. A knight has $8$ possible ways to move once. So I believe there are $8^{10}= 2^{30} \sim 1$ billion permutations. How many in which the knight ends up on the same square?

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