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 A189628 Fixed point of the morphism 0->001, 1->010. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS 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. 0->001, 1->010..A189628..A189629..A189630..A189631 0->001, 1->011..A116178..A189636..A189637..A189638 0->001, 1->100..A189632..A189633..A189634..A189635 0->001, 1->101..A189640..A026138..A026323..A189641 0->001, 1->110..A064990..A189658..A189659..A189660 0->010, 1->001..A189664..A189665..A189666..A189667 0->010, 1->011..A080846..A026225..A026179..A189672 0->010, 1->100..A189668..A189669..A189670..A189671 0->010, 1->101..A000035..A005408..A005843..A004526 0->010, 1->110..A189673..A026227..A026138..A189674 0->011, 1->001..A189706..A189707..A189708..A189709 0->011, 1->010..A156595..A189715..A189716..A189717 0->011, 1->100..A189718..A189719..A189720..A189721 0->011, 1->101..A189723..A189724..A189725..A189726 0->011, 1->110..A189727..A189728..A189729..A189730 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. REFERENCES J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003. LINKS FORMULA a(3k-2)=0, a(3k-1)=a(k), a(3k)=1-a(k) for k>=1. - corrected by Michel Dekking, Sep 09 2022 EXAMPLE 0->001->001001010->-> MATHEMATICA 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*) CROSSREFS Cf. A189629, A189630, A189631, A189576. Sequence in context: A143518 A122414 A288216 * A289239 A188432 A282317 Adjacent sequences: A189625 A189626 A189627 * A189629 A189630 A189631 KEYWORD nonn AUTHOR Clark Kimberling, Apr 24 2011 STATUS approved

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Last modified December 6 10:03 EST 2022. Contains 358630 sequences. (Running on oeis4.)