A formula for the generating functions of powers of Horadam's sequence

@article{Mansour2004AFF,
  title={A formula for the generating functions of powers of Horadam's sequence},
  author={Toufik Mansour},
  journal={Australasian J. Combinatorics},
  year={2004},
  volume={30},
  pages={207-212}
}
The second-order linear recurrence sequence (wn(a, b; p, q))n≥0, or briefly (wn)n≥0, is defined by wn+2 = pwn+1 + qwn, (1) with w0 = a, w1 = b and n ≥ 0. This sequence was introduced in 1965 by Horadam [3, 4], and it generalizes many sequences (see [1, 5]). Examples of such sequences are Fibonacci number sequences (Fn)n≥0, Lucas number sequences (Ln)n≥0, and Pell number sequences (Pn)n≥0, when one has p = q = b = 1, a = 0; p = q = b = 1, a = 2; and p = 2, q = b = 1, a = 0; respectively. In this… CONTINUE READING

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