A pattern sequence approach to Stern’s sequence
نویسندگان
چکیده
منابع مشابه
A pattern sequence approach to Stern's sequence
Let w ∈ 1{0, 1} * and let a w (n) be the number of occurrences of the word w in the binary expansion of n. Let {s(n)} n0 denote the Stern sequence, defined by s(0) = 0, s(1) = 1, and for n 1 s(2n) = s(n), and s(2n + 1) = s(n) + s(n + 1). In this note, we show that s(n) = a 1 (n) + w∈1{0,1} * s([w] 2)a w1 (n) where w denotes the complement of w (obtained by sending 0 → 1 and 1 → 0) and [w] 2 den...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.07.029