Let the sequence
be generated as follows with
and for
1.) Determine the maximum and minimum value of
over
and find all
for which these extreme values are attained.
2.) How many terms
are equal to 0?
%V0
Let the sequence $a(n), n = 1,2,3, \ldots$ be generated as follows with $a(1) = 0,$ and for $n > 1:$
$$a(n) = a\left( \left \lfloor \frac{n}{2} \right \rfloor \right) + (-1)^{\frac{n(n+1)}{2}}.$$
1.) Determine the maximum and minimum value of $a(n)$ over $n \leq 1996$ and find all $n \leq 1996$ for which these extreme values are attained.
2.) How many terms $a(n), n \leq 1996,$ are equal to 0?
Školjka