A091521 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 the center of one of the 6 faces of the combination cube.

1, 4, 12, 28, 84, 212, 632, 1544, 4584, 11220, 33060, 80152, 234648, 565192, 1643552, 3926832, 11337422, 26852656, 76981660

Offset: 0

Author

Hugo Pfoertner, Jan 19 2004

Keywords

• fini
• hard
• more
• nonn

Comments

See under A090577.

Examples

			a(1)=4 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 one of the 4 adjacent cubes located at the edges of the face initially containing the empty space. The cube at the center of the combination cube cannot replace the empty space because the construction of this puzzle inhibits the movement of the central cube.
		

Crossrefs

Cf. A090577, A090578 this puzzle with different initial configurations, A090572 2 X 2 X 2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.

Programs

Python

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=13)) # Michael S. Branicky, Dec 28 2020

Extensions

a(14)-a(18) from Michael S. Branicky, Dec 28 2020