Question 77
Consider the sequence $y_0, y_1, \dots$ such that $y_0 = -\frac{1}{4}$ and $y_1 = 0$, and furthermore
$$
y_{n+1} + y_{n-1} = 4y_n + 1
$$
for all $n \ge 1$. Prove that for all $n \ge 0$ the expression $2y_{2n} + \frac{3}{2}$ is
a) a positive integer, and
b) 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 $2y_{2n} + \frac{3}{2}$ is
a) a positive integer, and
b) the square of an integer.