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$\sum_{n=1}^\infty \frac {2^{\left \lfloor \sqrt n \right \rceil} +2^{- \left \lfloor \sqrt n \right \rceil}}{2^n} = \ ?$

$$

Notation: $\lfloor \cdot \rceil$ denotes the nearest integer function.

@Adhiraj Dutta asked me to solve this problem.

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