Composition writing

Discrete Mathematics Level 5

A composition of a positive integer \(n\) is an ordered sequence of positve integers that sum to \(n.\) A part of a composition refers to one of the numbers in the ordered sequence. For example, the ordered sequence \( 3, 3, 2 \) is a composition of 8 which has 3 parts.

What is the total number of parts in all of the compositions of the number 8?

Details and assumptions

\((1,2,1\)) and \((2,1,1)\) are different compositions of 4, because the order of the elements is different.


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