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

0,2

Comments

See under A090573.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A090572 2 X 2 X 2 puzzle, A090573, A090574, A090575 3 X 3 X 3 puzzle with different initial configurations.

Sequence in context: A104525 A126986 A341990 * A152174 A087206 A275863

Adjacent sequences: A090573 A090574 A090575 * A090577 A090578 A090579

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