Recognizing a Factoring Pattern (Pt. 2)

Question

I am trying to identify a pattern in the following set of equations;

$N_{-1}=1$

$N_{0}=2y$

$N_{1}=2y^2+z$

$N_{2}=2y^3+3yz$

$N_{3}=2y^4+5y^2 z+z^2$

$N_{4}=2y^5+7y^3 z+4yz^2$

$N_{5}=2y^6+9y^4 z+9y^2 z^2+z^3$

I need to express $N_h$. Any assistance would be greatly appreciated.

Answer 1

might be $$ N_{j+2} = y N_{j+1} + z N_j $$

Try it