A090578 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 mid-edge of one of the 12 edges of the combination cube.

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

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 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, fixed=13)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (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