Torsion formula for triangle-square chain graphs

Let $G_{t,s^k}$ be the graph obtained by gluing a triangle and $k$ squares in a sequence along edges, with $v=3+2k$ vertices. Torsion formula for $G_{t,s^k}$.

$$\operatorname{tor} H^{1,4k+2}_{{\mathcal A}_3}(G_{t,s^k})=\mathbb{Z}_3^{2k}.$$

This is one of the computational conjectures in the paper, and no resolution is reported.