How can I express Second-order Fibonacci number with usual Fibonacci numbers?

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Second-order Fibonacci numbers are defined as follows:

$$ S_0 = 0; S_1 = 1; S_n = S_{n-1} + S_{n-2} + F_n $$

How can I express $S_n$ in terms of the usual Fibonacci numbers $F_n$ and $F_{n+1}$?