A080602 Number of positions in which the 3 X 3 X 3 Rubik's cube puzzle can be after exactly n quarter-turns.

1, 12, 114, 1068, 10011, 93840, 878880, 8221632, 76843595, 717789576, 6701836858, 62549615248, 583570100997, 5442351625028, 50729620202582, 472495678811004, 4393570406220123, 40648181519827392, 368071526203620348

Offset

0,2

Comments

This is the number of positions that can be reached in n quarter-turns from the start, but which cannot be reached in fewer than n quarter-turns. (A half-turn counts as two moves.)

The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003

References

Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.

Rokicki, Tomas. Thirty years of computer cubing: The search for God's number. 2014. Reprinted in "Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rogers", ed. Thane Plambeck and Tomas Rokicki, MAA Press, 2020, pp. 79-98. See Table 9.5.

Links

Table of n, a(n) for n=0..18.

Alan Bawden, Cube Lovers Archive, Part 15

Alan Bawden, Cube Lovers Archive, Part 26

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

Tomas Rokicki, God's Algorithm out to 15q*. Posted Sep 26 2009. - Tomas Rokicki, Jul 14 2010

Thomas Scheunemann, God's Algorithm out to 16q*. Posted Jul 09 2010. - Tomas Rokicki, Jul 14 2010

Thomas Scheunemann, God's Algorithm out to 17q*. Posted Jul 09 2010. - Tomas Rokicki, Jul 14 2010

Tomas Rokicki, God's Algorithm out to 18q*. Posted Jul 19 2014.

Crossrefs

Cf. A005452, A080583, A080601, A080638.

Sequence in context: A154237 A006635 A062386 * A333299 A090250 A199702

Adjacent sequences: A080599 A080600 A080601 * A080603 A080604 A080605

Keyword

nonn,fini

Author

N. J. A. Sloane, Feb 25 2003

Extensions

Added a(14) and a(15) from my earlier investigations, confirmed by Scheunemann, and also added his result for a(16). - Tomas Rokicki, Jul 14 2010

Added a(17) from Thomas Scheunemann, a(18) from my God's Number investigations, corrected some links. - Tomas Rokicki, Sep 01 2014

Name edited by Charles R Greathouse IV, Jan 19 2016

Status

approved