In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be zero. Here, we show that that does not generalize. Instead, the (necessary) condition in the cases considered is that the first momentum \emph{plus a nonlinear correction term} must be zero.