We study some ratios related to hyper-Horadam numbers such as Wnr/Wn-1r while n→∞ by using a symmetric algorithm obtained by the recurrence relation ank=ank-1+an-1k, where Wnr is the nth hyper-Horadam number. Also, we give some special cases of these ratios such as the golden ratio and silver ratio.
In this paper, we compute the spectral norms of r− circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms) and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms. Moreover, we give some examples related to special cases of our results.
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