OFFSET
0,2
COMMENTS
a(n) = Sum_{i=0..n} (-1)^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 A020986, 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.
EXAMPLE
For n = 4, a(n) = 1+1+1+1+(-1) = 3.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Feb 10 2023
STATUS
approved