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A189628
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Fixed point of the morphism 0->001, 1->010.
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27
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0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0
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OFFSET
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1
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COMMENTS
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A189628 is one of many 01-sequences fixed by morphisms. An extension of the list begun at A189576 is continued here with sequences of type 3,3.
Each row shows a morphism, followed by four sequences:
(1) the fixed sequence a [starting from a(0)=0],
(2) positions of 0 in a,
(3) positions of 1 in a,
(4) partial sums of a.
Some lower-numbered entries are conjectural.
Each of the 15 sequences in column 3 (i.e., A189628 to A189727) is generated by a 3-part recurrence, as in the Formula section. Two other sequences generated by such a recurrence are A189816 and A189820.
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.
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LINKS
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FORMULA
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a(3k-2)=0, a(3k-1)=a(k), a(3k)=1-a(k) for k>=1. - corrected by Michel Dekking, Sep 09 2022
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EXAMPLE
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0->001->001001010->->
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MATHEMATICA
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t = Nest[Flatten[# /. {0->{0, 0, 1}, 1->{0, 1, 0}}] &, {0}, 5] (*A189628*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189629*)
Flatten[Position[t, 1]] (*A189630*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189631*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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