- #1

luke8ball

- 22

- 0

## Homework Statement

For n ≥ 1, let g(n) be the number of ways to write n as the sum of

the integers in a sequence of any length, where each integer in the sequence is at least 2.

For n≥3, show that g(n) = g(n-1) + g(n-2).

**2. The attempt at a solution**

I've gone through values of g(n) for small values of 'n,' and it's clear to me that the recurrence relation is the same as that of the Fibonacci, with different starting values of 'n.' However, to prove the relation, I'm trying to split an arbitrary g(n) into two disjoint cases. I feel like somehow I must show that g(n) can be manipulated into two different contexts, one which is the exact same as g(n-1), and another the same as g(n-2). Any ideas? I can't think of how to split this into two cases.