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A189661 Fixed point of the morphism 0->010, 1->10 starting with 0. 11
0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

From Michel Dekking, Oct 20 2018: (Start)

Let alpha=(3-sqrt(5))/2 be the 'small golden mean'.

The following two facts follow from Proposition 2 and Theorem 2 in my paper on substitution invariant words.

(I) The sequence {a(n)} is the inhomogeneous Sturmian sequence

    s'(alpha,1-alpha) = (ceiling(n*alpha+1-alpha)-ceiling((n-1)*alpha+1-alpha)).

(II) The other fixed point of 0->010, 1->10 is the inhomogeneous Sturmian sequence

    A289034 = s(alpha,1-alpha) = (floor(n*alpha+1-alpha)-floor((n-1)*alpha+1-alpha)).

a(n) = A289034(n) for all n > 2, but a(1),a(2) = 0,1; A289034(1),A289034(2) = 1,0.

(End)

REFERENCES

Bernardino, André, Rui Pacheco, and Manuel Silva. "Coloring factors of substitutive infinite words." Discrete Mathematics 340.3 (2017): 443-451. See Example 2.

LINKS

Table of n, a(n) for n=1..144.

A. Bernardino, M. Silva, R. Pacheco, Coloring factors of substitutive infinite words, arXiv:1605.09343 [math.CO], 2016.

Michel Dekking, Substitution invariant Sturmian words and binary trees, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A17.

EXAMPLE

0->010->01010010->1001001010010->...

MATHEMATICA

t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{1, 0}}] &, {0}, 5] (*A189661*)

f[n_] := t[[n]]

Flatten[Position[t, 0]] (*A189662*)

Flatten[Position[t, 1]] (*A026356*)

s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;

Table[s[n], {n, 1, 120}] (*A189663*)

CROSSREFS

Cf. A189662, A026356, A189663.

Sequence in context: A285966 A215530 A241422 * A145573 A092202 A285686

Adjacent sequences:  A189658 A189659 A189660 * A189662 A189663 A189664

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 25 2011

EXTENSIONS

Name corrected by Michel Dekking, Oct 18 2018

STATUS

approved

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)