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%I #9 Dec 29 2020 06:32:14
%S 1,6,24,72,192,624,2004,6504,19776,62760,186000,583712,1720972,
%T 5344088,15565416,47816092,137916958
%N Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space in the center of the combination cube.
%C See under A090573.
%e a(1)=6 because the empty space in the center of the cube present in the assumed initial configuration can be replaced by any of the 6 adjacent cubes from the face centers in the first move.
%o (Python) # uses alst(), swap() in A089473, moves3d() in A090573
%o moves = lambda p, shape: moves3d(p, shape)
%o start, shape = "123456789ABCD-EFGHIJKLMNOPQ", (3, 3, 3)
%o print(alst(start, shape, maxd=12)) # _Michael S. Branicky_, Dec 28 2020
%Y A090572 2 X 2 X 2 puzzle, A090573, A090575, A090576 3 X 3 X 3 puzzle with different initial configurations.
%K fini,hard,more,nonn
%O 0,2
%A _Hugo Pfoertner_, Jan 15 2004
%E a(13)-a(16) from _Michael S. Branicky_, Dec 28 2020
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