The total number of ordered trees with three nodes

Question

I get mixed answers online

• https://in.answers.yahoo.com/question/index?qid=20100508110438AAbKyMj
• http://wiki.answers.com/Q/How_many_ordered_trees_are_possible_with_3_nodes?#slide=2

I also saw the question in https://stackoverflow.com/a/3/312969/129 , but that didn't help me

What should be the answer?

• Also is this a tree?

      a
     /
    b
   /
  c
  

Answer 1

Refer to the following link for a really good article on counting the number of ordered trees.

Answer 2

, , - , , "", . , ( ) .

-, , , , . , ( , ), , , , . , .

. , , , . node ( ) , .

. - A, B, C, ( ).

N, . T (N) , N () .

: N = 1. node, , node . , T (1) = 1.

: N = 2. node. node . , T (2) = 2.

: N = 3. node. node, :

• A: node , . , . , 3 * 2 = 6 , , node .

• B: node , . T (2) = 2 , 3 * 2 = 6 , , node .

( ), : T (3) = 6 + 6 = 12.

, , , , . , , :

: N. . N - 1 . , N - 1 ( N - 1 ). , . , , .

, . , , .

.. , , , -

    A                      A
   /                        \
  B           and            B
 /                            \
C                              C

, . , ( node , ). , . , , - . B. C. , .