

A060010


Number of 2nmove sequences on a 3 X 3 X 3 Rubik's Cube (only quartertwists 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 nth term is equal to the sum of the nth 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




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



