Problem 1845. Pascal's pyramid

Created by Tim

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>In Pascal's triangle each number is the sum of the two nearest numbers in the line above:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 1\n 1 1\n 1 2 1\n 1 3 3 1\n 1 4 6 4 1]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A three-dimensional analog of Pascal's triangle can be defined as a square pyramid in which each number is the sum of the four nearest numbers in the layer above. Define a function</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>pascalp(n)</w:t></w:r><w:r><w:t> that returns the nth layer of this pyramid, as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ pascalp(1)\n 1\n pascalp(2)\n 1 1\n 1 1\n pascalp(3)\n 1 2 1\n 2 4 2\n 1 2 1\n pascalp(4)\n 1 3 3 1\n 3 9 9 3\n 3 9 9 3\n 1 3 3 1\n pascalp(5)\n 1 4 6 4 1\n 4 16 24 16 4\n 6 24 36 24 6\n 4 16 24 16 4\n 1 4 6 4 1]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note: Pascal's pyramid can also be defined as a tetrahedron (see</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Pascal%27s_pyramid\"><w:r><w:t>http://en.wikipedia.org/wiki/Pascal%27s_pyramid</w:t></w:r></w:hyperlink><w:r><w:t>), in which case the layers are triangular rather than square, and the numbers are the trinomial coefficients.</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>"}]}

In Pascal's triangle each number is the sum of the two nearest numbers in the line above:<pre> 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1</pre>A three-dimensional analog of Pascal's triangle can be defined as a square pyramid in which each number is the sum of the four nearest numbers in the layer above. 
Define a function <tt>pascalp(n)</tt> that returns the nth layer of this pyramid, as follows:<pre> pascalp(1)
 1
 pascalp(2)
 1 1
 1 1
 pascalp(3)
 1 2 1
 2 4 2
 1 2 1
 pascalp(4)
 1 3 3 1
 3 9 9 3
 3 9 9 3
 1 3 3 1
 pascalp(5)
 1 4 6 4 1
 4 16 24 16 4
 6 24 36 24 6
 4 16 24 16 4
 1 4 6 4 1</pre>Note: Pascal's pyramid can also be defined as a tetrahedron (see <a href = "http://en.wikipedia.org/wiki/Pascal%27s_pyramid">http://en.wikipedia.org/wiki/Pascal%27s_pyramid</a>), in which case the layers are triangular rather than square, and the numbers are the trinomial coefficients.

Solve

Solution Stats

158 Solutions
87 Solvers

Last Solution submitted on Mar 27, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Solution 309847

1 Comment

1 Comment

Andrew Newell on 24 Aug 2013

Beautiful!

Problem Recent Solvers87

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 1845. Pascal's pyramid

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers87

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Problem 1845. Pascal's pyramid

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers87

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Players