Upper Bounds for Stern's Diatomic Sequence and Related Sequences
نویسنده
چکیده
Let (s2(n)) ∞ n=0 denote Stern’s diatomic sequence. For n > 2, we may view s2(n) as the number of partitions of n − 1 into powers of 2 with each part occurring at most twice. More generally, for integers b, n > 2, let sb(n) denote the number of partitions of n− 1 into powers of b with each part occurring at most b times. Using this combinatorial interpretation of the sequences sb(n), we use the transfer-matrix method to develop a means of calculating sb(n) for certain values of n. This then allows us to derive upper bounds for sb(n). In the special case b = 2, our bounds improve upon the current upper bounds for the Stern sequence. We then show that lim sup n→∞ sb(n) nlogb φ = (b2 − 1)logb φ √ 5 .
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عنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016