Question 173
Consider the sequence $y_0, y_1, \ldots$ with $y_0 = -\frac{1}{4}$ and $y_1 = 0$ which further satisfies
$$y_{n+1} + y_{n-1} = 4y_n + 1$$
for all $n \ge 1$. Prove that for all $n \ge 0$ the expression $2y_{2n} + \frac{3}{2}$
a) is a positive integer and
b) is the square of an integer.
$$y_{n+1} + y_{n-1} = 4y_n + 1$$
for all $n \ge 1$. Prove that for all $n \ge 0$ the expression $2y_{2n} + \frac{3}{2}$
a) is a positive integer and
b) is the square of an integer.