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%I #10 Dec 29 2020 06:33:30
%S 1,4,10,30,74,222,546,1628,3978,11810,28658,84520,203562,596520,
%T 1425924,4150232,9838116,28418002,66805554
%N Number of configurations of a variant 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-edge of one of the 12 edges of the combination cube.
%C See under A090577.
%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, fixed=13)
%o start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
%o print(alst(start, shape, maxd=13)) # _Michael S. Branicky_, Dec 28 2020
%Y Cf. A090577, A091521 this puzzle with different initial configurations, A090572 2X2X2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.
%K fini,hard,more,nonn
%O 0,2
%A _Hugo Pfoertner_, Jan 19 2004
%E a(14)-a(18) from _Michael S. Branicky_, Dec 28 2020
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