For any positive integer $N$, consider the Fibonacci sequence $F_n$ of length $N$. Using $F_n$ we can define a Fibonacci discrete probability distribution as follows:
$$p_N(n)=\frac{F_n}{\sum_{k=1}^N F_k}\ \ \forall n=1,2,\ldots,N$$
$$p_N(n)=\frac{F_{N+1-n}}{\sum_{k=1}^N F_k}\ \ \forall n=1,2,\ldots,N$$
With the increasing sequence probability distribution (first equation), and the second equation (associated with decreasing sequence) the question is what is the Entropy of those Distributions. Thank you in advance.