A090574 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.

1, 6, 24, 72, 192, 624, 2004, 6504, 19776, 62760, 186000, 583712, 1720972, 5344088, 15565416, 47816092, 137916958

Offset: 0

Author

Hugo Pfoertner, Jan 15 2004

Keywords

• fini
• hard
• more
• nonn

Comments

See under A090573.

Examples

			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.
		

Crossrefs

A090572 2 X 2 X 2 puzzle, A090573, A090575, 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 = "123456789ABCD-EFGHIJKLMNOPQ", (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