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The behavior of the vector recurrence y" + i = Afyn + wn+1 is studied under very weak assumptions. Let \(Af) denote the spectral radius of M and let \(M) > 1. Then if the wn are bounded in norm and a certain subspace hypothesis holds, the root order of the yn is shown to be \(M).doi:10.1090/s0025-5718-1977-0426464-0 fatcat:xkyt4m6ieze37hkgcjg4ylfv6u