

A090578


Number of configurations of a variant of the 3dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at midedge of one of the 12 edges of the combination cube.


3



1, 4, 10, 30, 74, 222, 546, 1628, 3978, 11810, 28658, 84520, 203562, 596520, 1425924, 4150232, 9838116, 28418002, 66805554
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OFFSET

0,2


COMMENTS

See under A090577.


LINKS

Table of n, a(n) for n=0..18.


EXAMPLE

a(1)=4 because the empty space located at midedge 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 midface 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, fixed=13)
start, shape = "123456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=13)) # Michael S. Branicky, Dec 28 2020


CROSSREFS

Cf. A090577, 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: A047188 A002220 A222807 * A007713 A058488 A036674
Adjacent sequences: A090575 A090576 A090577 * A090579 A090580 A090581


KEYWORD

fini,hard,more,nonn


AUTHOR

Hugo Pfoertner, Jan 19 2004


EXTENSIONS

a(14)a(18) from Michael S. Branicky, Dec 28 2020


STATUS

approved



