where $E=\left\{ M_1=[2], M_2=[2], M_3=[2,2] \right\}$.

-   $T_{10}=M(T)_E=\left( \begin{matrix} 0 & 1 & 2 \\ 0 & 0 & 1 \\ 0 &0 & 0 \end{matrix}\right)$ where $E=\left\{ M_1=[2], M_2=[2], M_3=[3] \right\}$.

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at(current bounding box.south)[$T_9$]{};

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at(current bounding box.south)[$T_{10}$]{};

It is easy to implement an algorithm that computes the number of untwisted Arf semigroups of $ \mathbb{N}^3$ with a given conductor. In the following table we have the values obtained for some conductors.

The following table contains the value of $|\overline{\textrm{Cond}(\textbf{c})}|$ for some values of $\textbf{c}$.

An algorithm for the Arf numerical semigroups with a given genus {#section4}
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In [@algo] it is presented an algorithm for the computation of the set of the Arf numerical semigroups with a given genus. In this section we give a new procedure for the computation of such a set that appeared to be faster when implemented in GAP.

First of all we recall some definitions and we fix some notations.\
A numerical semigroup $S$ is a submonoid of $(\mathbb{N},+)$ such that $ \mathbb{N} \setminus S$ is finite. The maximum $F(S)$ of the set $ \mathbb{Z} \setminus S$ is known as the Frobenius number of $S$. The conductor $c(S)$ of $S$ is the 