A NOTE ON SUM OF k-TH POWER OF HORADAM’S SEQUENCE
نویسنده
چکیده
(1) wn+2 = pwn+1 + qwn, with given w0 = a,w1 = b and n ≥ 0. This sequence was introduced, in 1965, by Horadam [Ho], and it generalizes many sequences (see [HW, HM]). Examples of such sequences are Fibonacci numbers sequence (Fn)n≥0, Lucas numbers sequence (Ln)n≥0, and Pell numbers sequence (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 paper we interested in studding the generating function for powers of Horadam’s sequence, that is, Hk(x; a, b, p, q) = Hk(x) = ∑ n≥0 w k nx .
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