Consider the recurrence relation $S_{n+2} = \ 3S_{n+1}-S_n$ with $s_1=\ s_2=\ 1$
Find its invariant of the form $S^2_{n+1}\ +\ aS_nS_{n+1}\ + \ bS^2_n$
Although i understand that the invariant is the form such that when a transformation is applied the result is unchanged, or in this case, the distance between each number in the sequence is the same but i am not sure where to start, is it simple mathematics? Squaring the first equation and messing around with it?