# Double nth-step Fibonacci summation

Number Theory Level 5

$\large \log_{8192} \left( \sum_{n=1}^{1729} \left ( \sum_{k=1}^\infty \frac{F_k ^n}{2^k} \right) +1 \right)$

let $$F^n_k$$ be the $$k^\text{th}$$ term of the $$n$$-step Fibonacci number. then evaluate the expression above.

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