Compositions with no 1
Discrete Mathematics
Level
4
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 \( C_{15} \).
by
Patrick Corn