Strong hub cover pebbling conjecture for cycles

In a cycle $C_n$, label the vertices counterclockwise as $v_1,v_2,\ldots,v_n$. Up to isomorphism, a vertex set in $C_n$ is a strong hub set if and only if it contains $v_1,v_2,\ldots,v_{n-2}$. Let $h_s^*(C_n)$ denote the strong hub cover pebbling number of $C_n$.

Strong hub cover pebbling conjecture for cycles.

$$h_s^*(C_n)=\begin{cases} 2^k+2^{k-1}-3, & \text{if } n=2k \text{ is even},\\ 2^{k+1}-3, & \text{if } n=2k+1 \text{ is odd}. \end{cases}$$

This conjecture gives the strong hub cover pebbling numbers for cycles according to the parity of their order; its resolution is not established in the supplied text.