Recently, Matsuhira, Matsusaka, and Tsuchida revisited old studies of the integrality of k-Göbel sequences and showed that the first 19 terms are always integers for every integer k ≥ 2. In this article, we further explore two topics: Ibstedt's (k, l)-Göbel sequences and Zagier's asymptotic formula for the 2-Göbel sequence, and extend their results.