The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)



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


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.


Cf. A054434.

Sequence in context: A263668 A053064 A171094 * A129583 A323839 A163585

Adjacent sequences:  A060007 A060008 A060009 * A060011 A060012 A060013




Alex Healy, Mar 15 2001



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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