Question 57
Let $a(1), a(2), \dots$ be the infinite sequence defined by:
$a(1) = a(2) = 1$ and
$$
a(n) = a(a(n-1)) + a(n - a(n-1)) \text{ for } n \ge 3.
$$
Prove that $a(2n) \le 2a(n)$ for all $n \ge 1$.
$a(1) = a(2) = 1$ and
$$
a(n) = a(a(n-1)) + a(n - a(n-1)) \text{ for } n \ge 3.
$$
Prove that $a(2n) \le 2a(n)$ for all $n \ge 1$.