A309070 - OEIS

%I #41 Nov 23 2019 13:44:02

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%C 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.

%H Patrick Poggensee, <a href="/A309070/a309070.jpg">Rubik Cube 90-90-flip Notes Description</a>

%H Patrick Poggensee, <a href="/A309070/a309070.png">Diagram Rubik's Cube 90 Degrees Flip Pattern All Sides</a> (the top side is assumed to be red)

%H Patrick Poggensee, <a href="/A309070/a309070_1.png">Graph Rubik's Cube 90-Degrees-Flip Sequence White Side</a>

%H Patrick Poggensee, <a href="https://www.youtube.com/watch?v=AKncpMi_JPY">Rubik's Cube 90 Degree Flip Pattern Sequence</a> (video)

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,-1,0,-1,0,-1,0,0,0,1,0,1,0,1,0,1,0,1).

%H <a href="/index/Ru#Rubik">Index entries for sequences related to Rubik cube</a>

%F 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

%t 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 *)

%K nonn,easy

%O 0,1

%A _Patrick Poggensee_, Jul 10 2019