A090575 - OEIS

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A090575

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 the center of one of the 6 faces of the combination cube.

1, 5, 17, 52, 164, 496, 1608, 5008, 16024, 48732, 153564, 460984, 1437632, 4263236, 13150544, 38498798, 117497284

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

See A090573.

LINKS

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

EXAMPLE

a(1)=5 because the empty space located at the center of a face of the combination cube in the assumed initial configuration can be replaced in the first move by either the cube from the center of the combination cube or by one of the 4 adjacent cubes located at the edges of the face initially containing the empty space.

PROG

(Python) # uses alst(), swap() in A089473, moves3d() in A090573

moves = lambda p, shape: moves3d(p, shape)

start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)

print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

CROSSREFS

A090572 2 X 2 X 2 puzzle, A090573, A090574, A090576 3 X 3 X 3 puzzle with different initial configurations.

Sequence in context: A178703 A248875 A037544 * A191139 A107167 A201478

Adjacent sequences: A090572 A090573 A090574 * A090576 A090577 A090578

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