Total number of nodes in a tree data structure?

Question

I have a tree data structure that is L levels deep each node has about N nodes. I want to work-out the total number of nodes in the tree. To do this (I think) I

Answer 1

The formula for calculating the amount of nodes in depth L is: (Given that there are N root nodes)

N^L

To calculate the number of all nodes one needs to do this for every layer:

for depth in (1..L)
    nodeCount += N ** depth

If there's only 1 root node, subtract 1 from L and add 1 to the total nodes count.

Be aware that if in one node the amount of leaves is different from the average case this can have a big impact on your number. The further up in the tree the more impact.

     *                *                 *         N ** 1
    ***              ***               ***        N ** 2
*** *** ***      *** *** ***       *** *** ***    N ** 3

This is community wiki, so feel free to alter my appalling algebra.