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$H(z)=1+2z^{-1}+z^{-2}$

We know the formula

$a_{m-1}\;(k)=\frac{a_m\;(k)-k_m\;a_m\;(m-k)}{1-k_m\;^2}$

Here $k_2=1$ That makes $a_{m-1}\;(k)=infinity$

How to find lattice coefficients of all pole IIR filter with filter coefficient $k_m$ is 1?

I have read this answer but it is not similar to this question

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