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URL: https://oeis.org/A360536

⇱ A360536 - OEIS

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A360536
Analog of Rudin-Shapiro sum sequence A020990, based on counting patterns 00 instead of 11.
1
1, 0, 1, 0, -1, -2, -1, -2, -1, 0, 1, 0, -1, -2, -1, -2, -3, -4, -5, -4, -5, -6, -5, -6, -5, -4, -3, -4, -5, -6, -5, -6, -5, -4, -3, -4, -3, -2, -3, -2, -1, 0, 1, 0, -1, -2, -1, -2, -3, -4, -5, -4, -5, -6, -5, -6, -5, -4, -3, -4, -5, -6, -5, -6, -7, -8, -9
OFFSET
0,6
COMMENTS
a(n) = Sum_{i=0..n} (-1)^(i+e(i)), where e(i) counts the (possibly overlapping) occurrences of 00 in the base-2 representation of n. Note that e(0) = 0. This is the analog of A020990, which is the same sum, but with e(n) replaced by the function that counts the (possibly overlapping) occurrences of 11 in the base-2 representation of n.
LINKS
N. Rampersad and J. Shallit, Rudin-Shapiro sums via automata theory and logic, Arxiv preprint arXiv:2302.00405 [math.NT], February 1 2023.
CROSSREFS
KEYWORD
sign
AUTHOR
Jeffrey Shallit, Feb 10 2023
STATUS
approved