Compositions with no 1

Probability Level 3

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 $C_{15}$ .