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%I #20 Feb 17 2024 10:08:06
%S 1,18,243,3240,43254,577368,7706988,102876480,1373243544,18330699168,
%T 244686773808,3266193870720,43598688377184,581975750199168,
%U 7768485393179328,103697388221736960,1384201395738071424,18476969736848122368,246639261965462754048,3292256598848819251200
%N Number of canonical sequences of moves of length n for the Rubik cube puzzle using the half-turn metric.
%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.
%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. Table 5.1 gives terms 0 through 20.
%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.
%F From _Colin Barker_, Mar 23 2020: (Start)
%F G.f.: (1 + 3*x)^2 / (1 - 12*x - 18*x^2).
%F a(n) = 12*a(n-1) + 18*a(n-2) for n>2.
%F a(n) = (-(6-3*sqrt(6))^n*(-3+sqrt(6)) + (3*(2+sqrt(6)))^n*(3+sqrt(6))) / 4 for n>0.
%F (End)
%Y Cf. A080601, A080602, A333299.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 23 2020
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