• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1439-1443
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• 2010

For a positive integer k $\geq$ 2, the k-bonacci sequence {$g^{(k)}_n$} is defined as: $g^{(k)}_1=\cdots=g^{(k)}_{k-2}=0$, $g^{(k)}_{k-1}=g^{(k)}_k=1$ and for n > k $\geq$ 2, $g^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n-2}+{\cdots}+g^{(k)}_{n-k}$. And the k-Lucas sequence {$l^{(k)}_n$} is defined as $l^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n+k-1}$ for $n{\geq}1$. In this paper, we give a representation of nth k-Lucas $l^{(k)}_n$ by using determinant.

• 호남수학학술지
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• 제34권4호
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• pp.533-548
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• 2012

We investigate relations of polynomials $x^n={\Sigma}^{n-1}_{i=0}x^i$ and recurrence sequences. We consider certain variations of the Fibonacci sequence and investigate explicit ways to compute the general nth term.