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%I #38 Aug 29 2020 02:20:48
%S 1,18,243,3240,43239,574908,7618438,100803036,1332343288,17596479795,
%T 232248063316,3063288809012,40374425656248,531653418284628,
%U 6989320578825358,91365146187124313
%N Number of positions in which the 3 X 3 X 3 Rubik's cube puzzle can be after exactly n moves, where a move is either a quarter-turn or a half-turn.
%C This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves.
%C The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003
%C Relationship with A080583: 243 = 262 - 18 - 1, 3240 = 3502 - 262, 43239 = 46741 - 3502, ...
%D Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 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 9.4.
%D Rokicki, T., Kociemba, H., Davidson, M., & Dethridge, J. (2014). The diameter of the rubik's cube group is twenty. SIAM REVIEW, 56(4), 645-670. See Table 5.1.
%H Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-25.gz">Cube Lovers Archive, Part 25</a>
%H Jerry Bryan, <a href="http://forum.cubeman.org/?q=node/view/68">God's Algorithm...</a>
%H David Dijon, <a href="https://www.youtube.com/watch?v=4g_OjRB0wCE">The insanely large number of Rubik's cube permutations | MegaFavNumbers</a>, video (2020)
%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://cubezzz.homelinux.org/drupal/?q=node/view/146">God's Algorithm out to 13f*</a>
%H Tomas Rokicki, <a href="http://cube20.org/">God's Number is 20</a>
%H T. Rokicki, <a href="http://dx.doi.org/10.1007/s00283-009-9105-3">Twenty-two moves suffice for Rubik's Cube</a>, Math. Intell. 32 (1) (2010) 33-40.
%H T. Rokicki, <a href="http://www.speedsolving.com/forum/showthread.php?t=22629">15f* in the Face Turn Metric.</a>
%H T. Rokicki, <a href="http://forum.cubeman.org/?q=node/view/191">God's Algorithm out to 14f*</a>
%H Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge, <a href="http://tomas.rokicki.com/rubik20.pdf">The Diameter Of The Rubik's Cube Group Is Twenty</a>, SIAM J. of Discrete Math, Vol. 27, No. 2 (2013), pp. 1082-1105.
%Y Cf. A080638, A005452, A080602.
%K nonn,fini
%O 0,2
%A _N. J. A. Sloane_, Feb 25 2003
%E a(11) (from Jerry Bryan, 2006) and a(12) (from Tom Rokicki, 2009) added by _Herbert Kociemba_, Jun 24 2009
%E a(13) added by _Tomas Rokicki_, Jul 25 2009
%E a(14) (from Thomas Scheunemann) and a(15) (from Morley Davidson, John Dethridge, _Herbert Kociemba_, and Tomas Rokicki) added by _Tomas Rokicki_, Jul 29 2010
%E Name edited by _Charles R Greathouse IV_, Jan 19 2016
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