OFFSET
0,2
COMMENTS
Here t and t^{-1} can be thought of as moves left and right, while a=a^{-1} represents the lighting or extinguishing of a lamp.
LINKS
Walter Parry, Growth series of some wreath products, Trans. Amer. Math. Soc., Vol. 331 (1992), No. 2, 751-759.
Index entries for linear recurrences with constant coefficients, signature (1, 3, 0, -5, -3, 2, 3, 1).
FORMULA
G.f.: (1+x)(1-x^2)^2*(1+x+x^2)/((1-x^2-x^3)^2*(1-x-x^2)).
EXAMPLE
Writing L and R for t and t^{-1}, there are 12 elements of the group which can be written as words of length 3, but not more briefly: LLL, LLa, LaL, LaR, aLL, aLa, aRa, aRR, RaL, RaR, RRa, and RRR.
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Woods, Jun 08 2017
STATUS
approved