科研之友
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摘要
Given k >= 2, let an, be the sequence defined by the recurrence a(n), = alpha(1)a(n-1) +i +...+ alpha(k)a(n-k) for n >= k, with initial values a(0) = a(1) = a(k-2) = a(k-2) = 0 and a(k- 1)= 1. We show under a couple of assumptions concerning the constants a, that the ratio n root a(n)/n-1 root a(n-1) is strictly decreasing for all n >= N, for some N depending on the sequence, and has limit 1. In particular, this holds in the cases when all of the are unity or when all of the alpha(i) are zero except for alpha(i) the first and last, which are unity. Furthermore, when k = 3 or k = 4, it is shown that one may take N to be an integer less than 12 in each of these cases.
- 出版日期2017-6
