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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