MathDB

Let the sequence a(n), n \equal{} 1,2,3, \ldots be generated as follows with a(1) \equal{} 0, and for

n > 1:

a(n) \equal{} a\left( \left \lfloor \frac{n}{2} \right \rfloor \right) \plus{} (\minus{}1)^{\frac{n(n\plus{}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?

Problem Statement