The sequence of integers is defined by and Prove that is odd for all
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The sequence $\{a_n\}$ of integers is defined by
$$a_1 = 2, a_2 = 7$$
and
$$- \frac {1}{2} < a_{n + 1} - \frac {a^2_n}{a_{n - 1}} \leq \frac {}{}, n \geq 2.$$
Prove that $a_n$ is odd for all $n > 1.$
Izvor: Međunarodna matematička olimpijada, shortlist 1988
Školjka 
of integers is defined by 
is odd for all 