Another Family of Fibonacci-Like Sequences
P.R.J. Asveld · The Fibonacci Quarterly · 1987
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 $\gamma_1$, . . . , $\gamma_k$.