Question 64
For a sequence $a_{1}, a_{2}, a_{3}, \ldots$ of real numbers it is known that
$$
a_{n} = a_{n-1} + a_{n+2} \quad \text{for } n = 2, 3, 4, \ldots
$$
What is the largest number of its consecutive elements that can all be positive?
$$
a_{n} = a_{n-1} + a_{n+2} \quad \text{for } n = 2, 3, 4, \ldots
$$
What is the largest number of its consecutive elements that can all be positive?