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A189576
Fixed point of the morphism 0->01, 1->110.
7
0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1
OFFSET
1
COMMENTS
A189576 is one of many 01-sequences fixed by morphisms. It is helpful to classify a few such sequences:
Type 2,2: morphism: 0->01, 1->10, A010060 (Thue-Morse)
..
Type 2,3: 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->01, 1->001..A189572..A189573..A080652..A088462
0->01, 1->010..A159684..A003152..A003151..A097508
0->01, 1->011..A096270..A026352..A004956..A005206
0->01, 1->100..A189476..A189477..A189478..A189575
0->01, 1->101..A189479..A007066..A099267..A189480
0->01, 1->110..A189576..A189577..A189578..A189579
..
Type 3,2: (rows as for type 2,3)
0->001, 1->01..A188432..A026351..A026352..A060144
0->001, 1->10..A189624..A189625..A189626..A189627
0->010, 1->01..A003849..A000201..A001950..A060144
0->010, 1->10..A189661..A189662..A026356..A189663
0->011, 1->01..A189687..A086377..A081477..A189688
0->011, 1->10..A189702..A189703..A189704..A189705
..
Type 3,3: (See A189628 for a list and discussion.)
EXAMPLE
0->01->01110->0111011011001->
MATHEMATICA
t = Nest[Flatten[# /. {0->{0, 1}, 1->{1, 1, 0}}] &, {0}, 6] (*A189576*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189577*)
Flatten[Position[t, 1]] (*A189578*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189579*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 23 2011
STATUS
approved