How to display number of filtered descendants in mptt?

Question

Django

There are following models using django-mptt:

from django.db import models
from mptt.models import MPTTModel, TreeForeignKey

# жанры
class Genre(MPTTModel):
    name = models.CharField(max_length=255, unique=True)
    parent = TreeForeignKey('self', on_delete=models.CASCADE, null=True, blank=True, related_name='children')

    class MPTTMeta:
        order_insertion_by = ['name']
        
# статьи        
class Article(models.Model):
    ...
    genre = TreeForeignKey(Genre, on_delete=models.CASCADE)
    published = models.BooleanField(default=False)

How to display a list of genres in a template along with the number of child articles, but filtered by published=True? The task is typical, it is not clear from the documentation.