# 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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