How Many Regular Ternary Ordered Trees with Height 3 Exist?

[fiksx]

TL;DR

I’m not too familiar with ordered tree. I’m solving excercise about tree but i’m not sure it is right or wrong

Summary: I’m not too familiar with ordered tree. I’m solving exercise about tree but i’m not sure it is right or wrong

How many regular ternary ordered tree with height 3 (ordered tree means children of each vertex are assigned a fixed ordering)? What is the smallest and biggest radius for tree with height k?

Attempt: For regular ternary ordered tree with height 3 There will be 9 node that will have children 9C1 +9C2+9C3+9C4+9C4+9C5+9C6+9C7+9C8+9C9

And smallest and biggest radius for tree with height

 

[jedishrfu]

Here's some discussion on k-ary trees that might help you check your answer:

https://cs.lmu.edu/~ray/notes/orderedtrees/

 

[fiksx]

Here's some discussion on k-ary trees that might help you check your answer:

https://cs.lmu.edu/~ray/notes/orderedtrees/

Thankyou but for ordered tree with height of 3 is the total possibility tree are 511? Because all sum possible combination of 9Ck (1<=k<=9) =511
Or other way multiplication of possibility in each subtree. First subtree will be 3C0 +3C1+3C2+3C3= 8 , because there are 3 subtree in height 1 so 8x8x8=512-1=511 , why substract 1 because 9C0 makes tree height 2 . Is this quite right?