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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 23 2020
STATUS
approved