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The relations among $$k$$-Fibonacci, $$k$$-Lucas and generalized $$k$$-Fibonacci numbers and the spectral norms of the matrices of involving these numbers. (English) Zbl 1265.11029
Summary: In this study, we obtain some relations among $$k$$-Fibonacci, $$k$$-Lucas and generalized $$k$$-Fibonacci numbers. Then we define circulant matrices involving $$k$$-Lucas and generalized $$k$$-Fibonacci numbers. At the end of this study, we investigate the upper and lower bounds for the norms of these matrices.
MSC:
 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 15B36 Matrices of integers