Exact feedback vertex number of generalized Sierpiński triangle graphs

Let $\hat{S_p^n}$ be the generalized Sierpiński triangle graph with integers $n\geq 3$ and $p\geq 4$, and let $f(G)$ denote the feedback vertex number of a graph $G$, namely the minimum number of vertices whose deletion makes $G$ acyclic. Feedback vertex number conjecture.

$$f(\hat{S_p^n})=\left\{\begin{array}{ll}p^n-\frac{p^{n-1}}{8}+\frac{p^{n-2}+\cdots+p}{8}+\frac{5p}{8}, & \text{if }p\text{ is even},\\ p^n-\frac{p^{n-1}+p^{n-2}-5p+3}{8}, & \text{if }p\text{ is odd}. \end{array}\right.$$

The preceding result gives an upper bound for $f(\hat{S_p^n})$ by constructing an induced forest, and the authors suspect that this bound is exact for all $n\geq 3$ and $p\geq 4$.