A333298 Number of canonical sequences of moves of length n for the Rubik cube puzzle using the half-turn metric.

1, 18, 243, 3240, 43254, 577368, 7706988, 102876480, 1373243544, 18330699168, 244686773808, 3266193870720, 43598688377184, 581975750199168, 7768485393179328, 103697388221736960, 1384201395738071424, 18476969736848122368, 246639261965462754048, 3292256598848819251200

Offset: 0

Author

N. J. A. Sloane, Mar 23 2020

Keywords

• nonn

References

• 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.
• 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.

Links

• Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge, The Diameter Of The Rubik's Cube Group Is Twenty, SIAM J. of Discrete Math, Vol. 27, No. 2 (2013), pp. 1082-1105.

Crossrefs

Cf. A080601, A080602, A333299.

Formula

From Colin Barker, Mar 23 2020: (Start)

G.f.: (1 + 3*x)^2 / (1 - 12*x - 18*x^2).

a(n) = 12*a(n-1) + 18*a(n-2) for n>2.

a(n) = (-(6-3*sqrt(6))^n*(-3+sqrt(6)) + (3*(2+sqrt(6)))^n*(3+sqrt(6))) / 4 for n>0.

(End)