%N 3D analog of A081113: the number of (n-1)-step paths a 3D chess king can make starting from one face of the n X n X n cube to the opposite one.
%C The rule is that the king can move in one step to any of the 26 (=3*3-1) adjacent positions; because we allow only solutions with n-1 steps, one component of the direction is enforced and only a choice of 9 different next steps remains; if the path is close to the cube surface, even fewer.
%C This is the square of A081113, because for both x and y coordinates you have A081113(n) possibilities for the path (and you can choose them independently). - _Robert Gerbicz_, Jun 11 2010
%e Example: for n=2, we can start from any of the 4 places on one face and move from there directly to any of the 4 positions on the opposite side: a(2) = 4*4 = 16.
%Y Cf. A081113.
%A _R. J. Mathar_, Jun 11 2010