[seqfan] Rook walk generates A081057?

[David Scambler]

Hello Seqfans,

A rook walk starts at the top left corner of a 4x4 board and stops when the path length reaches n. Any square may be revisited. 
a(n) = number of possible walks of length n = 1,2,6,18,58,186,602... = A081057? 
I have checked this programmatically up to n = 16. E&OE

Is this already known? I could not find any applications of A081057.

dave