A090575 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 the center of one of the 6 faces of the combination cube.

1, 5, 17, 52, 164, 496, 1608, 5008, 16024, 48732, 153564, 460984, 1437632, 4263236, 13150544, 38498798, 117497284

Offset: 0

Author

Hugo Pfoertner, Jan 15 2004

Keywords

• fini
• hard
• more
• nonn

Comments

See A090573.

Examples

			a(1)=5 because the empty space located at the center of a face of the combination cube in the assumed initial configuration can be replaced in the first move by either the cube from the center of the combination cube or by one of the 4 adjacent cubes located at the edges of the face initially containing the empty space.
		

Crossrefs

A090572 2 X 2 X 2 puzzle, A090573, A090574, A090576 3 X 3 X 3 puzzle with different initial configurations.

Programs

Python

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

Extensions

a(13)-a(16) from Michael S. Branicky, Dec 28 2020