Volume 34 • Number 1 • 2011   • A Matrix Approach for General Higher Order Linear Recurrences Emrah Kiliç and Pantelimon Stanica Abstract. We consider k sequences of generalized order-k linear recurrences with arbitrary initial conditions and coefficients, and we give their generalized Binet formulas and generating functions. 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. 2010 Mathematics Subject Classification: 11B37, 40C05, 15A36, 15A15. Full text: PDF