BG-MO 2003 Problem 3

Given the sequence $\{y_n\}_{n=1}^{\infty}$ defined by $y_1=y_2=1$ and $$y_{n+2} = (4k-5)y_{n+1}-y_n+4-2k, n\ge1$$ find all integers $k$ such that every term of the sequence is a perfect square.