OFFSET
0,2
COMMENTS
The group is presented by <a, t | 1 = [a, t^(-k) a t^k], for all k>.
LINKS
Walter Parry, Growth series of some wreath products, Trans. Amer. Math. Soc. 331 (1992), 751-759.
Index entries for linear recurrences with constant coefficients, signature (4, -2, -4, -4, 4, 6, 4, 1).
FORMULA
G.f.: (1-x)^2 (1+x)^3 (1+x^2) / ((1-2x-x^2)(1-x-x^2-x^3)^2).
EXAMPLE
a(2)=17, since the elements of length up to 2 are 1, a, a^-1, t, t^-1, a^2, at, at^-1, a^-2, a^-1t, a^-1t^-1, ta, ta^-1, t^2, t^-1a, t^-1a^-1, t^-2.
MATHEMATICA
CoefficientList[ Series[-((x^2 + 1) (x - 1)^2 (x + 1)^3)/((x^3 + x^2 + x - 1)^2 (x^2 + 2 x - 1)), {x, 0, 27}], x] (* or *)
LinearRecurrence[{4, -2, -4, -4, 4, 6, 4, 1}, {1, 5, 17, 53, 153, 421, 1125, 2937}, 28] (* Robert G. Wilson v, Aug 08 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zoran Sunic, Nov 08 2017
STATUS
approved