Question 9
A9 (POL) Let the sequence $a(n)$, $n=1,2,3,\ldots$, be generated as follows: $a(1)=0$, and for $n\gt 1$,
$$a(n)=a([n/2])+(-1)^{\frac{n(n+1)}2}.$$
(Here $[t]$ = the greatest integer $\le t$.)
(a) Determine the maximum and minimum value of $a(n)$ over $n\le1996$ and find all $n\le1996$ for which these extreme values are attained.
(b) How many terms $a(n)$, $n\le1996$, are equal to $0$?
$$a(n)=a([n/2])+(-1)^{\frac{n(n+1)}2}.$$
(Here $[t]$ = the greatest integer $\le t$.)
(a) Determine the maximum and minimum value of $a(n)$ over $n\le1996$ and find all $n\le1996$ for which these extreme values are attained.
(b) How many terms $a(n)$, $n\le1996$, are equal to $0$?