A090576 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.

1, 4, 12, 40, 128, 412, 1251, 4026, 12362, 39624, 120012, 379132, 1130914, 3530916, 10402781, 32112656, 93427431

Offset: 0

Author

Hugo Pfoertner, Jan 15 2004

Keywords

• fini
• hard
• more
• nonn

Comments

See under A090573.

Examples

			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.
		

Crossrefs

Cf. A090572 2 X 2 X 2 puzzle, A090573, A090574, A090575 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 = "1-23456789ABCDEFGHIJKLMNOPQ", (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