Trac #29134: node_number_at_depth broken for binary trees

{{{
sage: ascii_art(BinaryTrees(3).list())
[ o    , o  ,   o  ,   o,     o ]
[  \      \    / \    /      /  ]
[   o      o  o   o  o      o   ]
[    \    /           \    /    ]
[     o  o             o  o     ]
sage: [t.node_number_at_depth(0) for t in BinaryTrees(3)]  # correct
[1, 1, 1, 1, 1]
sage: [t.node_number_at_depth(1) for t in BinaryTrees(3)]  # expected
[1, 1, 2, 1, 1]
[2, 2, 2, 2, 2]
sage: [t.node_number_at_depth(2) for t in BinaryTrees(3)]  # expected
[1, 1, 0, 1, 1]
[2, 2, 4, 2, 2]
}}}

This comes from the fact that the empty tree thinks it has 1 node at
depth 0:
{{{
sage: T = BinaryTree()
sage: T
.
sage: T.is_empty()
True
sage: T.node_number_at_depth(0)
1
}}}

URL: https://trac.sagemath.org/29134
Reported by: gh-mwageringel
Ticket author(s): Travis Scrimshaw
Reviewer(s): Markus Wageringel

src/sage/combinat/abstract_tree.py

@@ -822,7 +822,21 @@ def node_number_at_depth(self, depth):
                    o
             sage: [T.node_number_at_depth(i) for i in range(6)]
             [1, 3, 4, 2, 1, 0]
+
+        TESTS:
+
+        Check that the empty tree has no nodes (:trac:`29134`)::
+
+            sage: T = BinaryTree()
+            sage: T
+            .
+            sage: T.is_empty()
+            True
+            sage: [T.node_number_at_depth(i) for i in range(3)]
+            [0, 0, 0]
         """
+        if self.is_empty():
+            return Integer(0)
         if depth == 0:
             return Integer(1)
         return sum(son.node_number_at_depth(depth - 1) for son in self)