login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
1, 3, 9, 24, 72, 174, 519, 1284, 3813, 9300, 27462, 66666, 195674, 470886, 1372946, 3280224, 9495005, 22487511, 64615934, 151714911 (list; graph; refs; listen; history; text; internal format)
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: A091587 A316892 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 16 03:46 EDT 2021. Contains 343937 sequences. (Running on oeis4.)