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 A140770 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. 0

%I

%S 1,16,289,4624,67081,902500,11471769,139570596,1640493009,18754206916,

%T 209576262025,2298031637476,24798178969729,263962539461776,

%U 2776718023652329,28909790108979264,298278580556192769,3052900712959977636,31023767417676585561,313247762072931012804

%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.

%K nonn

%O 1,2

%A _R. J. Mathar_, Jun 11 2010

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Last modified December 7 19:54 EST 2021. Contains 349585 sequences. (Running on oeis4.)