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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

Table of n, a(n) for n=0..94.

Patrick Poggensee, Rubik Cube 90-90-flip Notes Description

Patrick Poggensee, Diagram Rubik's Cube 90 Degrees Flip Pattern All Sides (the top side is assumed to be red)

Patrick Poggensee, Graph Rubik's Cube 90-Degrees-Flip Sequence White Side

Patrick Poggensee, Rubik's Cube 90 Degree Flip Pattern Sequence (video)

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).

Index entries for sequences related to Rubik cube

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: A200280 A198363 A253267 * A010544 A198869 A094130

Adjacent sequences:  A309067 A309068 A309069 * A309071 A309072 A309073

KEYWORD

nonn,easy

AUTHOR

Patrick Poggensee, Jul 10 2019

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)