# Compositions with no 1

**Discrete Mathematics**Level 5

A composition of \( n \) is an expression of \( n \) as a sum of not necessarily distinct positive integers, where the order matters. Note that \( n = n \) counts as a composition of \( n \).

Let \( C_n \) be the number of *compositions* of \( n \) with no part equal to 1.

For instance, \( C_6 = 5 \) because \( 6 = 6 =4+2=3+3=2+4=2+2+2.\)

Find \( C_{15} \).