A matrix approach for general higher order linear recurrences
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We consider k sequences of generalized order-k linear recurrences with arbitrary initial condition and coefficients, and we give their generalized Bine formula and genertaing fucntion. We also obtain a new matrix method to derive explicit formulas for the sums of terms of the k sequences. Further, some relationships between determinants of certain Hessenberg matrices and the terms of these sequences are obtained.