Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Feb 21 2023 07:32:17
%S 0,1,2,1,2,3,4,3,4,3,2,1,2,3,4,3,4,5,6,7,8,9,10,9,10,9,8,7,8,9,10,9,
%T 10,9,8,7,6,5,4,3,4,3,2,1,2,3,4,3,4,5,6,7,8,9,10,9,10,9,8,7,8,9,10,9,
%U 10,11,12,13,14,15,16,17,16,17,18,19,20,21,22
%N Analog of the Moser-Newman sum sequence A005599, but counting 0's (instead of 1's) in the binary representation of 3*n.
%H J. Shallit, <a href="https://arxiv.org/abs/2302.09436">Rarefied Thue-Morse sums via automata theory and logic</a>, arXiv:2302.09436 [math.NT], February 18 2023.
%F a(n) = Sum_{i=0..n-1} (-1)^A080791(3*i).
%Y Cf. A005599, A080791.
%K nonn
%O 0,3
%A _Jeffrey Shallit_, Feb 18 2023