A060010 Number of 2n-move sequences on the 3 X 3 X 3 Rubik's Cube (only quarter-twists count as moves) that leave the cube unchanged.

1, 12, 312, 10464, 398208, 16323072, 702465024

Offset

0,2

Comments

I.e., closed walks of length 2n from a fixed vertex on the Cayley graph of the cube with {F, F^(-1), R, R^(-1), B, B^(-1), L, L^(-1) U, U^(-1), D, D^(-1)} as the set of generators. Alternatively, the n-th term is equal to the sum of the n-th powers of the eigenvalues of this Cayley graph divided by the order of the Rubik's cube group, ~4.3*10^19 (see A054434).

Links

Table of n, a(n) for n=0..6.

Example

There are 12 closed walks of length 2: F*F^(-1), F^(-1)*F, R*R^(-1), R^(-1)*R, ..., D*D^(-1), D^(-1)*D.

Crossrefs

Cf. A054434, A061713, A080602.

Sequence in context: A263668 A053064 A171094 * A129583 A323839 A163585

Adjacent sequences: A060007 A060008 A060009 * A060011 A060012 A060013

Keyword

hard,nonn,more

Author

Alexander D. Healy, Mar 15 2001

Status

approved