A090577 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 one of the enclosing cube corners.

1, 3, 9, 24, 72, 174, 519, 1284, 3813, 9300, 27462, 66666, 195674, 470886, 1372946, 3280224, 9495005, 22487511, 64615934, 151714911

Offset

0,2

Comments

The sliding cube 3 X 3 X 3 puzzle under consideration has a fixed central block and 25 movable blocks that can be shifted in the space between the enclosing holder frame and the central block. A description is given in US patents 3845959 and 6513808.

Links

Table of n, a(n) for n=0..19.

Chih Chung Fang, Cubic Puzzle. US Patent 6513808, filed May 09, 2001

Daniel Kosarek, Three-dimensional block puzzle. US Patent 3845959, filed Nov. 5, 1974

Example

a(1)=3 because the empty space at one of the 6 corners in the assumed initial configuration can be replaced by any of the 3 adjacent cubes from the middle of the 3 edges meeting at the empty corner in the first move.

Prog

(Python) # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "-123456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=14)) # Michael S. Branicky, Dec 28 2020

Crossrefs

Cf. A090578, 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.

Sequence in context: A316892 A346295 A018047 * A047114 A290511 A103301

Adjacent sequences: A090574 A090575 A090576 * A090578 A090579 A090580

Keyword

fini,hard,more,nonn

Author

Hugo Pfoertner, Jan 19 2004

Extensions

a(15)-a(19) from Michael S. Branicky, Dec 28 2020

Status

approved