# Knights to Infinity

A knight is placed at the center of an infinitely large chess board. For large $$n,$$ the number of squares on which the knight can be after exactly $$n$$ moves is asymptotically $$a \cdot n^b$$ for real numbers $$a$$ and $$b.$$ Find $$a+b.$$

Note: A chess knight moves in an "L" shape either 1 square vertically and 2 squares horizontally or 2 squares vertically and 1 square horizontally, as indicated by the stars above.

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