[WordPress API] About the 'count' field of get_terms function

get_terms is a very common function in WordPress. Here is the definition:
get_terms( array|string $args = array(),  array $deprecated = '' )

For example:
$res = get_terms(term->taxonomy, array('parent' => term->id, 'hide_empty' => false));
var_dump($res);

The WordPress will print something like this:

array (size=5)
  0 => 
    object(WP_Term)[4319]
      public 'term_id' => int 15
      public 'name' => string 'Copenhagen S' (length=12)
      public 'slug' => string 'copenhagen-s' (length=12)
      public 'term_group' => int 0
      public 'term_taxonomy_id' => int 15
      public 'taxonomy' => string 'property_city' (length=13)
      public 'description' => string '' (length=0)
      public 'parent' => int 37
      public 'count' => int 3
      public 'filter' => string 'raw' (length=3)
  1 => 
    object(WP_Term)[4317]
      public 'term_id' => int 24
      public 'name' => string 'Copenhagen SV' (length=13)
      public 'slug' => string 'copenhagen-sv' (length=13)
      public 'term_group' => int 0
      public 'term_taxonomy_id' => int 24
      public 'taxonomy' => string 'property_city' (length=13)
      public 'description' => string '' (length=0)
      public 'parent' => int 37
      public 'count' => int 0
      public 'filter' => string 'raw' (length=3)
  2 => 
    object(WP_Term)[4304]
      public 'term_id' => int 14
      public 'name' => string 'Copenhagen V' (length=12)
      public 'slug' => string 'copenhagen-v' (length=12)
      public 'term_group' => int 0
      public 'term_taxonomy_id' => int 14
      public 'taxonomy' => string 'property_city' (length=13)
      public 'description' => string '' (length=0)
      public 'parent' => int 37
      public 'count' => int 0
      public 'filter' => string 'raw' (length=3)
  3 => 
    object(WP_Term)[4303]
      public 'term_id' => int 20
      public 'name' => string 'Nordhavn' (length=8)
      public 'slug' => string 'nordhavn' (length=8)
      public 'term_group' => int 0
      public 'term_taxonomy_id' => int 20
      public 'taxonomy' => string 'property_city' (length=13)
      public 'description' => string '' (length=0)
      public 'parent' => int 37
      public 'count' => int 2
      public 'filter' => string 'raw' (length=3)
  4 => 
    object(WP_Term)[4301]
      public 'term_id' => int 22
      public 'name' => string 'Valby' (length=5)
      public 'slug' => string 'valby' (length=5)
      public 'term_group' => int 0
      public 'term_taxonomy_id' => int 22
      public 'taxonomy' => string 'property_city' (length=13)
      public 'description' => string '' (length=0)
      public 'parent' => int 37
      public 'count' => int 0
      public 'filter' => string 'raw' (length=3)

The field 'count' will be a little confusing as actually it doesn't represent the number of all the posts belonging to the specific term, but the number of posts only directly belonging to it -- which means the posts belonging to its child terms will not be counted in this number.

So if the 'count' of a term FATHER_TERM is 3, and the term has 2 child terms A and B. The total number of its posts should be: FATHER_TERM->count + A->count + B->count

We can calculate this by using a recursion function like this:

function count_posts_by_term($terms) {

    $sub_terms = get_terms( $terms->taxonomy, array(

                'parent' => $terms->term_id,

                'hide_empty' => false,

            )   

    );  

    if(count($sub_terms) > 0) {

        $sum = $terms->count;

        foreach ($sub_terms as $sub) {

            $sum +=  count_posts_by_term($sub);

        }   

        return $sum;

    } else {

        return $terms->count;

    }   

}