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%I #28 May 20 2023 16:28:08
%S 2,8,16,12,32,24,19,28,64,48,38,36,34,29,48,52,128,96,76,72,74,54,56,
%T 52,64,53,48,41,84,64,83,108,256,192,152,144,146,108,110,100,144,114,
%U 96,74,102,78,82,84,120,96,87,76,86,71,66,61,154,120,94,84,138,109,176,212,512,384,304,288,292,216
%N Number of states in the minimal deterministic finite automaton with output generating the n-fold running sum (mod 2) of the Thue-Morse sequence (A010060).
%C The 0-fold running sum of A010060 is A010060. To generate the n-fold running sum {c(k)} from the (n-1)-fold running sum {b(k)}, define c(0) = b(0) and c(k+1) = (c(k) + b(k+1)) mod 2.
%H Jeffrey Shallit and Anatoly Zavyalov, <a href="https://arxiv.org/abs/2303.15203">Transduction of Automatic Sequences and Applications</a>, arXiv:2303.15203 [cs.FL], 2023, see p. 21.
%F a(2^n) = 2^(n+3) (Proof in Shallit and Zavyalov). - _Anatoly Zavyalov_, Mar 30 2023
%Y Cf. A010060.
%K nonn
%O 0,1
%A _Jeffrey Shallit_, Dec 22 2022
%E More terms from _Anatoly Zavyalov_, Mar 30 2023