• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1439-1443
• /
• 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.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.533-548
• /
• 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.