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%I #22 Mar 23 2020 04:06:25
%S 1,12,114,1068,10011,93840,878880,8221632,76843595,717789576,
%T 6701836858,62549615248,583570100997,5442351625028,50729620202582,
%U 472495678811004,4393570406220123,40648181519827392,368071526203620348
%N Number of positions in which the 3 X 3 X 3 Rubik's cube puzzle can be after exactly n quarter-turns.
%C 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.)
%C The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003
%D Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.
%D 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.
%H Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-15.gz">Cube Lovers Archive, Part 15</a>
%H Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-26.gz">Cube Lovers Archive, Part 26</a>
%H Mark Longridge, <a href="http://cubeman.org/fullcube.txt">God's Algorithm Calculations for Rubik's Cube...</a>
%H Tomas Rokicki, <a href="http://forum.cubeman.org/?q=node/view/153">God's Algorithm out to 15q*</a>. Posted Sep 26 2009. - _Tomas Rokicki_, Jul 14 2010
%H Thomas Scheunemann, <a href="http://forum.cubeman.org/?q=node/view/194">God's Algorithm out to 16q*</a>. Posted Jul 09 2010. - _Tomas Rokicki_, Jul 14 2010
%H Thomas Scheunemann, <a href="http://forum.cubeman.org/?q=node/view/195">God's Algorithm out to 17q*</a>. Posted Jul 09 2010. - _Tomas Rokicki_, Jul 14 2010
%H Tomas Rokicki, <a href="http://forum.cubeman.org/?q=node/view/535">God's Algorithm out to 18q*</a>. Posted Jul 19 2014.
%Y Cf. A005452, A080583, A080601, A080638.
%K nonn,fini
%O 0,2
%A _N. J. A. Sloane_, Feb 25 2003
%E 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
%E Added a(17) from Thomas Scheunemann, a(18) from my God's Number investigations, corrected some links. - _Tomas Rokicki_, Sep 01 2014
%E Name edited by _Charles R Greathouse IV_, Jan 19 2016
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