Given matrices $A_{n\times n}, B_{n\times m}, C_{m\times m}$ such that $A^iBC^{N-i}$ is matrix with all zeros except upper right element for all $i$ from $0$ to $N$, what can we say about Frobenius norm of sum $\left\|\sum_{i=0}^NA^iBC^{N-i}\right\|$?