ACMS reciprocal-sum formulas for negative generalized Fibonacci parameters

Let $f_n(s,t)$ be the generalized Fibonacci sequence, let $\mathbb{Z}^+$ denote the positive integers, and let $\lfloor\cdot\rfloor$ be the floor function. ACMS conjecture. If $s>t\ge1$, $(s,-t)\ne(2,-1)$, and $n,r\in\mathbb{Z}^+$, then

$$\left\lfloor\left(\sum_{k=n}^{\infty}\frac{1}{f_{rk}(s,-t)}\right)^{-1}\right\rfloor=f_{rn}(s,-t)-f_{r(n-1)}(s,-t)-1.$$

If $t=-1$ and $s,n,r\in\mathbb{Z}^+$, then

$$\left\lfloor\left(\sum_{k=n}^{\infty}\frac{1}{f_{rk}(s,-1)^2}\right)^{-1}\right\rfloor=f_{rn}(s,-1)^2-f_{r(n-1)}(s,-1)^2-1.$$

These formulas are presented as the conjectured analogue for negative parameters of the preceding reciprocal-sum theorem. The supplied text gives no resolution evidence.