Fibonacci Number by Power of 2

Theorem
where:
 * $F_n$ denotes the $n$th Fibonacci number
 * $\dbinom n {2 k + 1} \ $ denotes a binomial coefficient.

Also presented as
This result can also be seen presented as:


 * $\ds 2^n F_n = 2 \sum_{k \text { odd} } \dbinom n k 5^{\paren {k - 1} / 2}$