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A309070 a(n) is the number of tiles of a chosen color on the front side of the Rubik Cube after n repetitions of the following procedure: rotate the right side by a 1/4 turn clockwise, then rotate the whole cube around the front-back axis by a 1/4 turn clockwise. 1
9, 6, 4, 3, 1, 1, 2, 2, 3, 5, 6, 6, 7, 4, 2, 2, 1, 2, 4, 4, 5, 5, 4, 4, 5, 3, 2, 3, 3, 4, 6, 4, 3, 3, 2, 3, 5, 4, 4, 5, 5, 4, 4, 2, 1, 2, 2, 4, 7, 6, 6, 5, 3, 2, 2, 1, 1, 3, 4, 6, 9, 6, 4, 3, 1, 1, 2, 2, 3, 5, 6, 6, 7, 4, 2, 2, 1, 2, 4, 4, 5, 5, 4, 4, 5, 3, 2, 3, 3, 4, 6, 4, 3, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The sequence takes values in the interval 1..9. We start from a completely solved cube and choose the color of the front side (say, white), so a(0)=9.
The sequence is periodic with period 60: after 60 moves the front side is complete again with 9 white tiles. The other 5 sides instead are scrambled.
LINKS
Patrick Poggensee, Diagram Rubik's Cube 90 Degrees Flip Pattern All Sides (the top side is assumed to be red)
Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1,0,-1,0,-1,0,0,0,1,0,1,0,1,0,1,0,1).
FORMULA
a(n) = - a(n-2) - a(n-4) - a(n-6) - a(n-8) + a(n-12) + a(n-14) + a(n-16) + a(n-18) + a(n-20) for n > 20. - Stefano Spezia, Jul 11 2019
MATHEMATICA
LinearRecurrence[{0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1}, {9, 6, 4, 3, 1, 1, 2, 2, 3, 5, 6, 6, 7, 4, 2, 2, 1, 2, 4, 4}, 100] (* Stefano Spezia, Jul 11 2019 *)
CROSSREFS
Sequence in context: A198363 A331550 A253267 * A010544 A343308 A198869
KEYWORD
nonn,easy
AUTHOR
Patrick Poggensee, Jul 10 2019
STATUS
approved

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Last modified March 28 03:28 EDT 2024. Contains 371235 sequences. (Running on oeis4.)