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%I #10 Dec 29 2020 06:33:15
%S 1,4,12,40,128,412,1251,4026,12362,39624,120012,379132,1130914,
%T 3530916,10402781,32112656,93427431
%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 at mid-side of one of the 12 edges of the combination cube.
%C See under A090573.
%e a(1)=4 because the empty space located at mid-edge of one of the 12 edges of the assumed initial configuration can be replaced in the first move by any of the adjacent 2 cubes from the same edge or by the adjacent mid-face cubes of the 2 faces forming this edge.
%o (Python) # uses alst(), swap() in A089473, moves3d() in A090573
%o moves = lambda p, shape: moves3d(p, shape)
%o start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
%o print(alst(start, shape, maxd=12)) # _Michael S. Branicky_, Dec 28 2020
%Y Cf. A090572 2 X 2 X 2 puzzle, A090573, A090574, A090575 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