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

0,2

Comments

See under A090573.

Links

Table of n, a(n) for n=0..16.

Example

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.

Prog

(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

Crossrefs

A090572 2 X 2 X 2 puzzle, A090573, A090575, A090576 3 X 3 X 3 puzzle with different initial configurations.

Sequence in context: A052749 A337021 A262445 * A294842 A290132 A297713

Adjacent sequences: A090571 A090572 A090573 * A090575 A090576 A090577

Keyword

fini,hard,more,nonn

Author

Hugo Pfoertner, Jan 15 2004

Extensions

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

Status

approved