A333299 Number of canonical sequences of moves of length n for the Rubik cube puzzle using the quarter-turn metric.

1, 12, 114, 1068, 10011, 93840, 879624, 8245296, 77288598, 724477008, 6791000856

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. Table 9.5 gives terms 0 through 18.

Links

Table of n, a(n) for n=0..10.

Formula

Conjectures from Colin Barker, Mar 23 2020: (Start)

G.f.: (1 + x)^4 / (1 - 8*x - 12*x^2 - 8*x^3 - 2*x^4).

a(n) = 8*a(n-1) + 12*a(n-2) + 8*a(n-3) + 2*a(n-4) for n>4.

(End)

Crossrefs

Cf. A080601, A080602, A333298.

Sequence in context: A006635 A062386 A080602 * A090250 A199702 A307820

Adjacent sequences: A333296 A333297 A333298 * A333300 A333301 A333302

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 23 2020

Status

approved