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11 -> 8 bytes
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ZippyMagician
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Arn -x, 1111 8 bytes

Ý®úŠ”→s©Ÿa'gŸ▀<Çúì═ 

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Explained

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

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

Arn -x, 11 bytes

Ý®úŠ”→s©Ÿa' 

Try it!

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 

Arn -x, 11 8 bytes

gŸ▀<Çúì═ 

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Explained

Unpacked: .=z^[1 1{+

 .= Rangify input (inclusive) z^  Zipped with exponentiation to [1 1{+  The fibonacci sequence, closing }] implied   Then take the sum 
Source Link
ZippyMagician
  • 1.7k
  • 10
  • 11

Arn -x, 11 bytes

Ý®úŠ”→s©Ÿa' 

Try it!

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