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A230603 Generalized Fibonacci word. Binary complement of A221150. 2
1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

Define strings S(0) = 1, S(1)= 110, thereafter S(n) = S(n-1)S(n-2); this sequence is the limit string S(infinity). See the examples below.

LINKS

Table of n, a(n) for n=0..80.

FORMULA

a(n) = floor((n + 2)/(3 - phi)) - floor((n + 1)/(3 - phi)), where phi = 1/2*(1 + sqrt(5)) is the golden ratio.

If we read the sequence as the decimal constant C = 0.11011 10110 11101 11011 01110 ... then C = sum {n >= 1} 1/10^floor(n*(3 - phi)).

9*C has the simple continued fraction expansion [0; 1, 110, 10^1, 10^3, 10^4, 10^7, ..., 10^Lucas(n), ...].

EXAMPLE

S(0) = 1

S(1) = 110

S(2) = 110 1

S(3) = 1101 110

S(4) = 1101110 1101

S(5) = 11011101101 1101110

The sequence of word lengths [1, 2, 4, 7, 11, 18, ...] is A000204.

MAPLE

Digits := 50: u := evalf((5-sqrt(5))/2): A230603 := n->floor((n+2)/u)-floor((n+1)/u): seq(A230603(n), n = 0..80);

CROSSREFS

Cf. A000204, A003849, A005614, A221150.

Sequence in context: A188090 A004547 A285358 * A229343 A085369 A188082

Adjacent sequences:  A230600 A230601 A230602 * A230604 A230605 A230606

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Nov 22 2013

STATUS

approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)