# Composition writing

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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