Arn -x, 11 bytes

Ý®úŠ”→s©Ÿa' 

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Explained

Unpacked: (=>\)z^[1 1{+

 (=>\) Fold with inclusive range ([a, b] → [a, a+1, ..., b-1, b]) z^ Zipped with exponentiation to [1 1{+ The fibonacci sequence, closing }] implied Then take the sum