A189576 Fixed point of the morphism 0->01, 1->110.

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.)

Links

Table of n, a(n) for n=1..120.

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

Cf. A189577, A189578, A189579, A189628.

Sequence in context: A278718 A130854 A165191 * A112448 A101264 A189723

Adjacent sequences: A189573 A189574 A189575 * A189577 A189578 A189579

Keyword

nonn

Author

Clark Kimberling, Apr 23 2011

Status

approved