Problem 44628. The other half of the Fibonacci sequence

Created by David Verrelli

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://mathworld.wolfram.com/FibonacciNumber.html\"><w:r><w:t>\"Fibonacci sequence\"</w:t></w:r></w:hyperlink><w:r><w:t> — F = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>circa</w:t></w:r><w:r><w:t> 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \"Fibonacci\")</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>circa</w:t></w:r><w:r><w:t> 1202 CE.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This sequence can be defined by</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>F(n+2) = F(n+1) + F(n)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>in which F(1) = 1, F(2) = 1, F(3) = 2, ....</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Later in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your job in this Cody Problem is to 'create history'(?) by extending this sequence to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>negative values of n</w:t></w:r><w:r><w:t>, to discover the missing half of this sequence!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>EXAMPLE:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You are only required to provide outputs for n &lt; 3 that can be represented by an</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://au.mathworks.com/help/matlab/ref/int64.html\"><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>int64</w:t></w:r></w:hyperlink><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://au.mathworks.com/help/matlab/numeric-types.html\"><w:r><w:t>data type</w:t></w:r></w:hyperlink><w:r><w:t>. To enforce this, your output needs to be of this data type.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

The <a href = "http://mathworld.wolfram.com/FibonacciNumber.html">"Fibonacci sequence"</a> — 
F = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from circa 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. "Fibonacci") circa 1202 CE.This sequence can be defined byF(n+2) = F(n+1) + F(n)in which F(1) = 1, F(2) = 1, F(3) = 2, ....Later in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).Your job in this Cody Problem is to 'create history'(?) by extending this sequence to negative values of n, to discover the missing half of this sequence!EXAMPLE:If n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.You are only required to provide outputs for n &lt; 3 that can be represented by an <a href = "https://au.mathworks.com/help/matlab/ref/int64.html"><tt>int64</tt></a> <a href = "https://au.mathworks.com/help/matlab/numeric-types.html">data type</a>. To enforce this, your output needs to be of this data type.

The <http://mathworld.wolfram.com/FibonacciNumber.html "Fibonacci sequence"> — 
F = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from _circa_ 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. "Fibonacci") _circa_ 1202 CE.

This sequence can be defined by

*F(n+2) = F(n+1) + F(n)*

in which F(1) = 1, F(2) = 1, F(3) = 2, ....

Later in history, it was recognised that F(0) = 0.  Of course, this still satisfies the formula in bold above [for n=0]:  F(2) = F(1) + F(0).

Your job in this Cody Problem is to 'create history'(?) by extending this sequence to _negative values of n_, to discover the missing half of this sequence!

EXAMPLE:

If n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.

You are only required to provide outputs for n < 3 that can be represented by an <https://au.mathworks.com/help/matlab/ref/int64.html |int64|> <https://au.mathworks.com/help/matlab/numeric-types.html data type>. To enforce this, your output needs to be of this data type.

Solve

Solution Stats

81 Solutions
16 Solvers

Last Solution submitted on Mar 04, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Solution 1584952

1 Comment

1 Comment

David Verrelli on 24 Jun 2019

Good job on commenting your code!

Problem Recent Solvers16

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44628. The other half of the Fibonacci sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers16

Suggested Problems

More from this Author32

Problem Tags

Community Treasure Hunt

Problem 44628. The other half of the Fibonacci sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers16

Suggested Problems

More from this Author32

Problem Tags

Community Treasure Hunt

Players