A090578 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.

1, 4, 10, 30, 74, 222, 546, 1628, 3978, 11810, 28658, 84520, 203562, 596520, 1425924, 4150232, 9838116, 28418002, 66805554

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 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. 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.

Programs

Python

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (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