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A189628
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Fixed point of the morphism 0->001, 1->010.
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26
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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.
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 A189320.
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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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Table of n, a(n) for n=1..122.
Index entries for sequences that are fixed points of mappings
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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, a(0)=0.
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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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Cf. A189629, A189630, A189631, A189576.
Sequence in context: A143518 A122414 A288216 * A289239 A188432 A282317
Adjacent sequences: A189625 A189626 A189627 * A189629 A189630 A189631
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Apr 24 2011
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STATUS
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approved
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