A080583 Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves.

1, 18, 262, 3502, 46741, 621649, 8240087, 109043123, 1441386411, 19037866206, 251285929522, 3314574738534, 43689000394782, 575342418679410

Offset

0,2

Comments

This is different from the sequence giving the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves (A080601).

A half-turn is considered to be a single move (rather than two moves).

The total number of positions is 901083404981813616.

Relationship with A080601: 243 = 262 - 18 - 1, 3240 = 3502 - 262, 43239 = 46741 - 3502, ...

Links

Table of n, a(n) for n=0..13.

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

Rokicki, Tomas; God's Algorithm out to 13f*

Crossrefs

Cf. A080601, A080602.

Sequence in context: A078205 A316698 A254248 * A273589 A076693 A083445

Adjacent sequences: A080580 A080581 A080582 * A080584 A080585 A080586

Keyword

nonn,more

Author

Alexander D. Healy, Feb 21 2003

Extensions

Added a(13). Tomas Rokicki, Jul 25 2009

Status

approved