There only exist 2 cent, 4 cent and 5 cent stamps. Provide a recurrence relation and the initial conditions to the number of ways to create $n$ cents in postage. I want to see the recurrence relation and the initial conditions. Also, calculate the number of permutations to come up with 20 cents in postage.
PLEASE DO NOT EDIT MY QUESTION THIS IS HOW IT IS ASKED
I have been struggling with this problem this is what I have come up with so far:
Recurrence relation: $f(n) = f(n - 2) + f(n-4) + f(n-5)$
Initial conditions: $a_0 = 1$ because you cant make 1 cent with 2, 4, 5 but you can make everything that comes after it. Then $a_1 = 2, a_2 = 4, a_3 = 5$.
permutations: $P(20,2) + P(20,4) + P(20,5) - overlap$. I am not sure how to calculate the overlap.
If anyone can give me some insight on my three steps it will be much appreciated!