An interesting question on Fibonacci series

I was thinking about an interesting question regarding the Fibonacci series. Here it is.
Assume that we draw the Fibonacci series of n as an inverted tree, where each node has its two additive terms as child nodes. For e.g. root node F(n) has F(n-1) and F(n-2) as children, and so on. Give an expression for the number of times node i occurs in the entire tree, where 1 <= i <= n.
Try to solve this problem. There is an interesting pattern to observe here.

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