Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two Moreno Frías, María Ángeles Rosales González, José Carlos Numerical semigroup Almost symmetric numerical semigroup Ideal I(S)-semigroup Genus Let S and T be two numerical semigroups. We say that T is an I(S)-semigroup if T\{0} is an ideal of S. Given k a positive integer, we denote by ∆(k) the symmetric numerical semigroup generated by {2, 2k + 1}. In this paper we present a formula which calculates the number of I(S)- semigroups with genus g(∆(k)) + h for some nonnegative integer h and which we will denote by i(∆(k), h). As a consequence, we obtain that the sequence {i(∆(k), h)}h∈N is never decreasing. Besides, it becomes stationary from a certain term. 2021-05-04T08:53:58Z 2021-05-04T08:53:58Z 2021 info:eu-repo/semantics/article Moreno-Frías, M.A.; Rosales, J.C. Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two. Symmetry 2021, 13, 794. https:// doi.org/10.3390/sym13050794 http://hdl.handle.net/10481/68295 10.3390/sym13050794 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI