$N$-extended affine Weyl groups are Weyl groups associated to $n$-extended affine root systems introduced by K. Saito . We calculate the growth series of the n-extended affine Weyl group of type $A_1$ with a generator system of an $n$-toroidal sense.
"The growth series of the $n$-extended affine Weyl group of type $A_1$." Proc. Japan Acad. Ser. A Math. Sci. 81 (3) 51 - 56, March 2005. https://doi.org/10.3792/pjaa.81.51