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%I #22 Jan 20 2025 22:50:13
%S 1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,
%T 1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,
%U 1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0
%N Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.
%e Triangle begins:
%e 1;
%e 0;
%e 1, 0;
%e 0, 1, 0, 1;
%e 1, 0, 1, 0, 0, 1, 0, 1;
%e 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
%e 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
%e ...
%t s = {1}; Do[s = Join[s, Mod[s + 1, 2]]; s = Join[s, s], {n, 4}]; s (* _Robert G. Wilson v_, Dec 22 2005 *)
%o (Python)
%o s = [1]
%o for _ in range(4):
%o s = s + [(x + 1) % 2 for x in s]
%o s = s + s
%o print(s) # _Robert C. Lyons_, Jan 19 2025
%o (PARI)
%o aiter(x) = my(s=[1]); for(i=1, x, s=concat(s, if(i%2, [1-e|e<-s], s))); s \\ _Ruud H.G. van Tol_, Jan 20 2025
%Y Cf. A112865 (as +-1), A341389 (complement).
%Y Cf. A104104, A010060.
%K easy,nonn,changed
%O 1,1
%A _Alexandre Losev_, Dec 15 2005
%E More terms from _Robert G. Wilson v_, Dec 22 2005