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Another Family of Fibonacci-like Sequences

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Asveld, Peter R.J. (1986) Another Family of Fibonacci-like Sequences. [Report]

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Abstract:We consider the family of difference equations $H_n = H_{n-1} + H_{n-2} + \sum_{j=0}^k \gamma n^{(j)}$ with $H_0 = H_1 = 1$, $n^{(j)} = n(n-1)(n-2)\cdots(n-j+1)$ for $j\geq1$ and $n^{(0)} = 1$. We express $H_n$ in terms of the Fibonacci numbers and in the parameters $\gamma_1$, . . . , $\gamma_k$.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/66052
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