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## Homework Statement

Let n be an odd integer ≥ 5. Find the number of triplets (x, y, z) of positive integers which satisfy the equation

x + y + 2z = n

## Homework Equations

Do not know

## The Attempt at a Solution

Let n = 2k + 1, k ≥ 2

x + y + 2z = n

2z = 2k + 1 - (x + y) ≤ 2k + 1 - 2 (because x + y ≥ 2)

2z ≤ 2k - 1

Then stuck

The answer is (n - 1)(n - 3)/4

Thanks