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A060010 Number of 2n-move sequences on a 3 X 3 X 3 Rubik's Cube (only quarter-twists count as moves) that leave the cube unchanged, 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). 1
1, 12, 312, 10464, 398208, 16323072, 702465024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

Sequence in context: A263668 A053064 A171094 * A129583 A323839 A163585

Adjacent sequences:  A060007 A060008 A060009 * A060011 A060012 A060013

KEYWORD

hard,nonn

AUTHOR

Alex Healy, Mar 15 2001

STATUS

approved

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Last modified December 8 12:28 EST 2021. Contains 349596 sequences. (Running on oeis4.)