A080617 - OEIS

%I #14 Jan 14 2025 15:55:23

%S 1,4,10,24,58,140,338,816,1909,4296,8893,17160,28891,37996,37678,

%T 27186,13051,4128,1199,372,122,36,10,2

%N Consider a 3 X 3 X 3 Rubik cube, but only allow the moves M_R, D; sequence gives number of positions that are exactly n moves from the start.

%C From _Ben Whitmore_, Dec 27 2024: (Start)

%C An alternative description is number of positions of the <U, M> subgroup of the Rubik cube at a distance of n moves from the solved state, in the slice-quarter-turn metric.

%C The slice-quarter-turn metric counts quarter-turns of outer faces and inner slices as 1 move, and half-turns of outer faces and inner slices as 2 moves.

%C The M slice is the middle layer between the left and the right faces, and an M move is a clockwise move of this slice when viewed from the left face.

%C The total number of positions is 6! * 2^5 * 4 * 2 = 184320.

%C The two positions requiring 23 moves can be reached by applying the following algorithm, or its inverse, to a solved cube: U M U M U M U M U' M U M' U M U M' U M U' M' U2 M. (End)

%H Mark Longridge, <a href="http://cubeman.org/fullcube.txt">God's Algorithm Calculations for Rubik's Cube...</a>

%Y Cf. A080601, A080614, etc.

%K nonn,fini,full

%O 0,2

%A _N. J. A. Sloane_, Feb 26 2003

%E a(11)-a(23) added by _Ben Whitmore_, Dec 27 2024