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.

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

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: A198363 A331550 A253267 * A010544 A343308 A198869

Adjacent sequences: A309067 A309068 A309069 * A309071 A309072 A309073

Keyword

nonn,easy

Author

Patrick Poggensee, Jul 10 2019

Status

approved