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.