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A309070
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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.
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1
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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