A pattern sequence approach to Stern’s sequence |
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Authors: | Michael Coons Jeffrey Shallit |
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Institution: | aUniversity of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, N2L 3G1, Canada;bUniversity of Waterloo, School of Computer Science, Waterloo, Ontario, N2L 3G1, Canada |
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Abstract: | Suppose that w∈1{0,1}∗ and let aw(n) be the number of occurrences of the word w in the binary expansion of n. Let {s(n)}n?0 denote the Stern sequence, defined by s(0)=0, s(1)=1, and for n?1, In this note, we show that where denotes the complement of w (obtained by sending 0?1 and 1?0) and w]2 denotes the integer specified by the word w∈{0,1}∗ interpreted in base 2. |
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Keywords: | Stern sequence Pattern sequence expansion |
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