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A060010
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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).
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1
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