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

0,2

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

Table of n, a(n) for n=0..19.

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.

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)

Crossrefs

Cf. A080601, A080602, A333299.

Sequence in context: A080629 A053540 A080601 * A016186 A081203 A016294

Adjacent sequences: A333295 A333296 A333297 * A333299 A333300 A333301

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2020

Status

approved