OFFSET
0,2
COMMENTS
The quarter-turn metric counts quarter-turns as 1 move and half-turns as 2 moves.
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.
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
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
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
Name edited by Ben Whitmore, Aug 02 2024
STATUS
approved