

A061713


Number of closed walks of length n on a 3 X 3 X 3 Rubik's Cube.


0



1, 0, 18, 36, 720, 3600, 42624, 312480, 3148032, 27073152, 261446688, 2407791936, 23168736768, 220481838720, 2137258661472
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OFFSET

0,3


COMMENTS

Number of nmove sequences on a 3 X 3 X 3 Rubik's Cube (quartertwists and halftwists count as moves, cf. A060010) that leave the cube unchanged, i.e. closed walks of length n from a fixed vertex on the Cayley graph of the cube with {F, F^(1), F^2, R, R^(1), R^2, B, B^(1), B^2, L, L^(1), L^2, U, U^(1), U^2, D, D^(1), D^2} 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).


LINKS

Table of n, a(n) for n=0..14.


EXAMPLE

There are 18 closed walks of length 2: F*F^(1), F^2*F^2, F^(1)*F, R*R^(1), R^(1)*R, R^2*R^2 . . ., D*D^(1), D^(1)*D, D^2*D^2.


CROSSREFS

Cf. A060010, A054434.
Sequence in context: A327774 A335784 A115550 * A198802 A041638 A041636
Adjacent sequences: A061710 A061711 A061712 * A061714 A061715 A061716


KEYWORD

hard,nonn,nice


AUTHOR

Alex Healy, Jun 21 2001


STATUS

approved



