A080638 Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves, up to equivalence under the full group of order 48 of the cube.

1, 2, 9, 75, 934, 12077, 159131, 2101575, 27762103, 366611212, 4838564147, 63818720716, 841134600018, 11076115427897

Offset

0,2

Comments

This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves.

A half-turn is considered to be 1 move.

The total number of inequivalent positions is 901083404981813616. - Jerry Bryan, Mar 03, 2003.

References

Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 1998.

Links

Table of n, a(n) for n=0..13.

Alan Bawden, Cube Lovers Archive, Part 25

Rokicki, Tomas; God's Algorithm out to 13f*

Crossrefs

This is A080601 reduced by action of group of order 48. Cf. A005452, A080602.

Sequence in context: A288581 A197082 A243054 * A375450 A370259 A335378

Adjacent sequences: A080635 A080636 A080637 * A080639 A080640 A080641

Keyword

nonn,fini

Author

N. J. A. Sloane, Feb 28 2003

Extensions

Added a(11)..a(13) Tomas Rokicki, Jul 25 2009

Status

approved