We present a new algorithm to explore or count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In the unleaved tree there are no leaves rather than the ones at depth equal to the genus in consideration. For exploring the unleaved tree we present a new encoding system of a numerical semigroup given by the gcd of its left elements and its shrinking, that is, the semigroup generated by its left elements divided by their gcd. We show a method to determine the right generators and strong generators of a semigroup by means of the gcd and the shrinking encoding, as well as a method to encode a semigroup from the encoding of its parent or of its predecessor sibling. With the new algorithm we obtained $n_{76}=29028294421710227$ and $n_{77}=47008818196495180$.

翻译：我们提出一种新算法，用于探索或计数给定亏格的数值半群。该算法采用数值半群树的无叶版本：在无叶树中，除深度等于待考虑亏格的节点外，不存在其他叶节点。为探索无叶树，我们提出一种基于左元素最大公约数及其收缩（即左元素除以最大公约数后生成的半群）的数值半群编码系统。我们展示了如何通过最大公约数与收缩编码确定半群的右生成元与强生成元，以及如何根据父节点或前驱兄弟节点的编码来编码当前半群。利用该新算法，我们得到 $n_{76}=29028294421710227$ 与 $n_{77}=47008818196495180$。