A080617 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.

1, 4, 10, 24, 58, 140, 338, 816, 1909, 4296, 8893, 17160, 28891, 37996, 37678, 27186, 13051, 4128, 1199, 372, 122, 36, 10, 2

Offset

0,2

Comments

From Ben Whitmore, Dec 27 2024: (Start)

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.

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.

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.

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

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)

Links

Table of n, a(n) for n=0..23.

Mark Longridge, God's Algorithm Calculations for Rubik's Cube...

Crossrefs

Cf. A080601, A080614, etc.

Sequence in context: A019494 A192886 A079844 * A080628 A225127 A230954

Adjacent sequences: A080614 A080615 A080616 * A080618 A080619 A080620

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Feb 26 2003

Extensions

a(11)-a(23) added by Ben Whitmore, Dec 27 2024

Status

approved