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Table 1 Numerical results of \(\pmb{a_{i}=F_{i}}\) , \(\pmb{r=1}\)

From: The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers

n

Theorem  2.1

Theorem  1.3

\(\frac{\mathbf{Third\ column}}{\mathbf{Second\ column}}\)

2

1

1

\(\frac{1}{1}=1\)

3

2

2

\(\frac{2}{2}=1\)

4

\(3\sqrt{2}\)

6

\(\frac{6}{3\sqrt{2}}=\sqrt{2}\)

5

\(\sqrt{60}\)

15

\(\frac{15}{\sqrt{60}}\approx1.936\)

6

\(\sqrt{200}\)

40

\(\frac{40}{\sqrt{200}}=2\sqrt{2}\)

n

\(\sqrt{(n-1)F_{n}F_{n-1}}\)

\(F_{n}F_{n-1}\)

\(\frac {F_{n}F_{n-1}}{\sqrt{(n-1)F_{n}F_{n-1}}}=\sqrt{\frac {F_{n}F_{n-1}}{n-1}}\)